The representation theory of the restricted rational Cherednik algebra for G₁₅

Computed by Ulrich Thiel using CHAMP (see LMS J. Comput. Math., 2015). Last update on Fri Mar 27 12:48:19 CET 2015.

Note: In the larger tables each cell has a mouseover tooltip providing information about the cell.

Quick navigation: Exceptional hyperplanes

For generic parameters

Non-singleton Calogero–Moser families

{ϕ_3,10'', ϕ_3,6', ϕ_3,2}, {ϕ_4,11, ϕ_4,5}, {ϕ_2,11'', ϕ_2,17, ϕ_2,5, ϕ_2,11'}, {ϕ_3,14, ϕ_3,10', ϕ_3,6''}, {ϕ_3,4, ϕ_3,12', ϕ_3,8'}, {ϕ_2,1, ϕ_2,7', ϕ_2,7'', ϕ_2,13}, {ϕ_4,7, ϕ_4,13}, {ϕ_3,8'', ϕ_3,16, ϕ_3,12''}, {ϕ_2,9, ϕ_2,15', ϕ_2,15'', ϕ_2,21}, {ϕ_4,3, ϕ_4,9}

Dimensions, Poincaré series and diagonal Verma multiplicities of the simple modules

ϕ	dim L(ϕ)	[Δ(ϕ) : L(ϕ)]	P_L(ϕ)
ϕ_1,0	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,6	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,8	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,14	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,16	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,22	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,12	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,18	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,20	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,26	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,28	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_1,34	288	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 12t¹² + 12t¹³ + 12t¹⁴ + 12t¹⁵ + 12t¹⁶ + 12t¹⁷ + 12t¹⁸ + 12t¹⁹ + 12t²⁰ + 12t²¹ + 12t²² + 12t²³ + 11t²⁴ + 10t²⁵ + 9t²⁶ + 8t²⁷ + 7t²⁸ + 6t²⁹ + 5t³⁰ + 4t³¹ + 3t³² + 2t³³ + t³⁴
ϕ_2,9	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,12	288	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 14t⁶ + 16t⁷ + 18t⁸ + 20t⁹ + 22t¹⁰ + 24t¹¹ + 22t¹² + 20t¹³ + 18t¹⁴ + 16t¹⁵ + 14t¹⁶ + 12t¹⁷ + 10t¹⁸ + 8t¹⁹ + 6t²⁰ + 4t²¹ + 2t²²
ϕ_2,15'	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,15''	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,18	288	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 14t⁶ + 16t⁷ + 18t⁸ + 20t⁹ + 22t¹⁰ + 24t¹¹ + 22t¹² + 20t¹³ + 18t¹⁴ + 16t¹⁵ + 14t¹⁶ + 12t¹⁷ + 10t¹⁸ + 8t¹⁹ + 6t²⁰ + 4t²¹ + 2t²²
ϕ_2,21	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,5	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,8	288	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 14t⁶ + 16t⁷ + 18t⁸ + 20t⁹ + 22t¹⁰ + 24t¹¹ + 22t¹² + 20t¹³ + 18t¹⁴ + 16t¹⁵ + 14t¹⁶ + 12t¹⁷ + 10t¹⁸ + 8t¹⁹ + 6t²⁰ + 4t²¹ + 2t²²
ϕ_2,11'	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,11''	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,14	288	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 14t⁶ + 16t⁷ + 18t⁸ + 20t⁹ + 22t¹⁰ + 24t¹¹ + 22t¹² + 20t¹³ + 18t¹⁴ + 16t¹⁵ + 14t¹⁶ + 12t¹⁷ + 10t¹⁸ + 8t¹⁹ + 6t²⁰ + 4t²¹ + 2t²²
ϕ_2,17	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,1	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,4	288	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 14t⁶ + 16t⁷ + 18t⁸ + 20t⁹ + 22t¹⁰ + 24t¹¹ + 22t¹² + 20t¹³ + 18t¹⁴ + 16t¹⁵ + 14t¹⁶ + 12t¹⁷ + 10t¹⁸ + 8t¹⁹ + 6t²⁰ + 4t²¹ + 2t²²
ϕ_2,7'	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,7''	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,10	288	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 14t⁶ + 16t⁷ + 18t⁸ + 20t⁹ + 22t¹⁰ + 24t¹¹ + 22t¹² + 20t¹³ + 18t¹⁴ + 16t¹⁵ + 14t¹⁶ + 12t¹⁷ + 10t¹⁸ + 8t¹⁹ + 6t²⁰ + 4t²¹ + 2t²²
ϕ_2,13	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_3,8'	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,2	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,8''	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,14	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,4	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,10''	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,16	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,10'	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,12'	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,6'	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,12''	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_3,6''	96	3	3 + 6t + 9t² + 12t³ + 12t⁴ + 12t⁵ + 12t⁶ + 12t⁷ + 9t⁸ + 6t⁹ + 3t¹⁰
ϕ_4,9	144	4	4 + 8t + 12t² + 16t³ + 20t⁴ + 24t⁵ + 20t⁶ + 16t⁷ + 12t⁸ + 8t⁹ + 4t¹⁰
ϕ_4,11	144	4	4 + 8t + 12t² + 16t³ + 20t⁴ + 24t⁵ + 20t⁶ + 16t⁷ + 12t⁸ + 8t⁹ + 4t¹⁰
ϕ_4,7	144	4	4 + 8t + 12t² + 16t³ + 20t⁴ + 24t⁵ + 20t⁶ + 16t⁷ + 12t⁸ + 8t⁹ + 4t¹⁰
ϕ_4,3	144	4	4 + 8t + 12t² + 16t³ + 20t⁴ + 24t⁵ + 20t⁶ + 16t⁷ + 12t⁸ + 8t⁹ + 4t¹⁰
ϕ_4,5	144	4	4 + 8t + 12t² + 16t³ + 20t⁴ + 24t⁵ + 20t⁶ + 16t⁷ + 12t⁸ + 8t⁹ + 4t¹⁰
ϕ_4,13	144	4	4 + 8t + 12t² + 16t³ + 20t⁴ + 24t⁵ + 20t⁶ + 16t⁷ + 12t⁸ + 8t⁹ + 4t¹⁰

Characters of the simple modules

ϕ	L(ϕ_1,0)	L(ϕ_1,6)	L(ϕ_1,8)	L(ϕ_1,14)	L(ϕ_1,16)	L(ϕ_1,22)	L(ϕ_1,12)	L(ϕ_1,18)	L(ϕ_1,20)	L(ϕ_1,26)	L(ϕ_1,28)	L(ϕ_1,34)	L(ϕ_2,9)	L(ϕ_2,12)	L(ϕ_2,15')	L(ϕ_2,15'')	L(ϕ_2,18)	L(ϕ_2,21)	L(ϕ_2,5)	L(ϕ_2,8)	L(ϕ_2,11')	L(ϕ_2,11'')	L(ϕ_2,14)	L(ϕ_2,17)	L(ϕ_2,1)	L(ϕ_2,4)	L(ϕ_2,7')	L(ϕ_2,7'')	L(ϕ_2,10)	L(ϕ_2,13)	L(ϕ_3,8')	L(ϕ_3,2)	L(ϕ_3,8'')	L(ϕ_3,14)	L(ϕ_3,4)	L(ϕ_3,10'')	L(ϕ_3,16)	L(ϕ_3,10')	L(ϕ_3,12')	L(ϕ_3,6')	L(ϕ_3,12'')	L(ϕ_3,6'')	L(ϕ_4,9)	L(ϕ_4,11)	L(ϕ_4,7)	L(ϕ_4,3)	L(ϕ_4,5)	L(ϕ_4,13)
ϕ_1,0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	1	0	1	1	0	0	1	0	1	1	0	0	1	0	0	1	1	0	1	0	0	0	0	0	0	1	0	0	1	1	1	0
ϕ_1,6	1	1	1	1	1	1	1	1	1	1	1	1	0	1	1	0	1	0	0	1	0	1	1	0	0	1	0	1	1	0	1	0	0	1	0	1	0	0	0	0	1	0	1	1	0	0	0	1
ϕ_1,8	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	1	0	0	1	0	0	1	1	0	1	0	0	1	1	0	0	0	1	0	1	1	0	1	0	0	0	0	1	0	1	0	1
ϕ_1,14	1	1	1	1	1	1	1	1	1	1	1	1	0	1	1	0	1	0	0	1	1	0	1	0	0	1	1	0	1	0	0	0	1	0	1	0	0	1	0	1	0	0	1	0	1	0	1	0
ϕ_1,16	1	1	1	1	1	1	1	1	1	1	1	1	0	1	0	0	1	1	0	1	0	0	1	1	1	1	0	0	1	0	1	0	0	0	0	0	0	1	0	1	1	0	1	1	1	0	0	0
ϕ_1,22	1	1	1	1	1	1	1	1	1	1	1	1	0	1	0	1	1	0	0	1	1	0	1	0	0	1	0	1	1	0	0	1	0	0	0	0	1	0	1	0	0	1	0	0	0	1	1	1
ϕ_1,12	1	1	1	1	1	1	1	1	1	1	1	1	0	1	0	0	1	1	0	1	0	0	1	1	0	1	0	0	1	1	1	0	0	1	0	0	1	0	0	1	0	0	0	0	1	1	1	0
ϕ_1,18	1	1	1	1	1	1	1	1	1	1	1	1	0	1	0	1	1	0	0	1	1	0	1	0	0	1	1	0	1	0	0	1	1	0	0	0	0	1	1	0	0	0	1	1	0	0	0	1
ϕ_1,20	1	1	1	1	1	1	1	1	1	1	1	1	0	1	0	0	1	1	1	1	0	0	1	0	1	1	0	0	1	0	0	1	0	0	1	0	0	1	0	0	1	0	0	1	0	1	0	1
ϕ_1,26	1	1	1	1	1	1	1	1	1	1	1	1	0	1	0	1	1	0	0	1	0	1	1	0	0	1	0	1	1	0	1	0	0	0	0	1	1	0	0	0	0	1	1	0	1	0	1	0
ϕ_1,28	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	1	0	1	1	0	0	1	0	0	1	0	0	1	1	0	0	1	0	0	1	0	0	1	0	0	1	1	1	1	0	0	0
ϕ_1,34	1	1	1	1	1	1	1	1	1	1	1	1	0	1	1	0	1	0	0	1	0	1	1	0	0	1	1	0	1	0	0	0	0	1	1	0	0	0	0	1	1	0	0	0	0	1	1	1
ϕ_2,9	2	2	2	2	2	2	2	2	2	2	2	2	1	2	1	0	2	0	0	2	0	1	2	1	0	2	1	0	2	1	0	0	0	2	1	1	1	0	1	1	1	0	0	1	0	2	1	2
ϕ_2,12	2	2	2	2	2	2	2	2	2	2	2	2	0	2	1	1	2	0	1	2	0	0	2	1	0	2	1	1	2	0	1	1	1	1	1	0	1	0	0	1	0	1	1	0	1	1	2	1
ϕ_2,15'	2	2	2	2	2	2	2	2	2	2	2	2	1	2	1	0	2	0	1	2	1	0	2	0	0	2	1	0	2	1	0	0	2	0	1	1	0	1	1	1	0	1	2	1	2	0	1	0
ϕ_2,15''	2	2	2	2	2	2	2	2	2	2	2	2	0	2	0	1	2	1	0	2	0	1	2	1	1	2	0	1	2	0	2	0	0	0	0	1	1	1	0	1	1	1	2	1	2	0	1	0
ϕ_2,18	2	2	2	2	2	2	2	2	2	2	2	2	1	2	0	0	2	1	0	2	1	1	2	0	1	2	0	0	2	1	1	1	1	1	0	1	0	1	1	0	1	0	1	2	1	1	0	1
ϕ_2,21	2	2	2	2	2	2	2	2	2	2	2	2	0	2	0	1	2	1	1	2	1	0	2	0	1	2	0	1	2	0	0	2	0	0	1	0	1	1	1	0	1	1	0	1	0	2	1	2
ϕ_2,5	2	2	2	2	2	2	2	2	2	2	2	2	1	2	1	0	2	0	1	2	0	1	2	0	0	2	0	1	2	1	1	0	1	1	0	2	0	0	1	0	1	1	2	2	1	0	0	1
ϕ_2,8	2	2	2	2	2	2	2	2	2	2	2	2	0	2	1	1	2	0	0	2	1	1	2	0	1	2	0	0	2	1	0	1	0	1	1	1	1	1	1	0	1	0	1	1	0	1	1	2
ϕ_2,11'	2	2	2	2	2	2	2	2	2	2	2	2	0	2	0	1	2	1	0	2	1	0	2	1	0	2	0	1	2	1	1	1	0	1	0	0	2	0	1	1	0	1	0	0	1	2	2	1
ϕ_2,11''	2	2	2	2	2	2	2	2	2	2	2	2	1	2	1	0	2	0	1	2	0	1	2	0	1	2	1	0	2	0	0	1	1	1	2	0	0	0	0	1	1	1	0	0	1	2	2	1
ϕ_2,14	2	2	2	2	2	2	2	2	2	2	2	2	1	2	0	0	2	1	1	2	0	0	2	1	0	2	1	1	2	0	1	0	1	0	1	1	1	1	0	1	0	1	1	1	2	1	1	0
ϕ_2,17	2	2	2	2	2	2	2	2	2	2	2	2	0	2	0	1	2	1	0	2	1	0	2	1	1	2	1	0	2	0	1	1	1	0	0	0	0	2	1	1	1	0	2	2	1	0	0	1
ϕ_2,1	2	2	2	2	2	2	2	2	2	2	2	2	1	2	0	1	2	0	1	2	0	1	2	0	1	2	0	1	2	0	1	1	1	0	1	1	1	0	0	0	0	2	1	0	2	1	2	0
ϕ_2,4	2	2	2	2	2	2	2	2	2	2	2	2	1	2	0	0	2	1	0	2	1	1	2	0	0	2	1	1	2	0	1	0	1	0	0	1	0	1	1	1	1	1	2	1	1	0	1	1
ϕ_2,7'	2	2	2	2	2	2	2	2	2	2	2	2	1	2	0	1	2	0	0	2	1	0	2	1	0	2	1	0	2	1	0	1	1	1	0	1	1	1	2	0	0	0	1	2	0	1	0	2
ϕ_2,7''	2	2	2	2	2	2	2	2	2	2	2	2	0	2	1	0	2	1	1	2	0	1	2	0	1	2	0	1	2	0	1	1	0	1	1	1	0	1	0	0	2	0	1	2	0	1	0	2
ϕ_2,10	2	2	2	2	2	2	2	2	2	2	2	2	0	2	1	1	2	0	1	2	0	0	2	1	1	2	0	0	2	1	0	1	0	1	1	0	1	0	1	1	1	1	0	1	1	2	1	1
ϕ_2,13	2	2	2	2	2	2	2	2	2	2	2	2	0	2	1	0	2	1	0	2	1	0	2	1	0	2	1	0	2	1	1	0	1	1	1	0	1	1	0	2	0	0	1	0	2	1	2	0
ϕ_3,8'	3	3	3	3	3	3	3	3	3	3	3	3	0	3	1	1	3	1	1	3	1	1	3	0	2	3	0	0	3	1	1	2	0	1	1	1	1	1	1	0	2	1	1	2	0	2	1	3
ϕ_3,2	3	3	3	3	3	3	3	3	3	3	3	3	1	3	0	1	3	1	1	3	0	1	3	1	0	3	1	2	3	0	2	1	1	0	1	1	1	1	0	1	1	2	2	1	3	1	2	0
ϕ_3,8''	3	3	3	3	3	3	3	3	3	3	3	3	1	3	1	1	3	0	0	3	1	1	3	1	1	3	0	0	3	2	0	1	1	2	1	1	1	1	2	1	1	0	1	2	0	2	1	3
ϕ_3,14	3	3	3	3	3	3	3	3	3	3	3	3	1	3	1	0	3	1	1	3	1	0	3	1	0	3	2	1	3	0	1	0	2	1	1	1	1	1	1	2	0	1	2	1	3	1	2	0
ϕ_3,4	3	3	3	3	3	3	3	3	3	3	3	3	2	3	0	0	3	1	1	3	1	1	3	0	0	3	1	1	3	1	1	0	2	1	1	2	0	1	1	1	1	1	3	2	2	0	1	1
ϕ_3,10''	3	3	3	3	3	3	3	3	3	3	3	3	0	3	2	1	3	0	1	3	0	1	3	1	1	3	1	0	3	1	0	1	1	2	2	1	1	0	1	1	1	1	0	1	1	3	2	2
ϕ_3,16	3	3	3	3	3	3	3	3	3	3	3	3	1	3	0	0	3	2	0	3	1	1	3	1	1	3	1	1	3	0	2	1	1	0	0	1	1	2	1	1	1	1	3	2	2	0	1	1
ϕ_3,10'	3	3	3	3	3	3	3	3	3	3	3	3	0	3	1	2	3	0	1	3	1	0	3	1	1	3	0	1	3	1	1	2	0	1	1	0	2	1	1	1	1	1	0	1	1	3	2	2
ϕ_3,12'	3	3	3	3	3	3	3	3	3	3	3	3	0	3	1	1	3	1	1	3	0	0	3	2	0	3	1	1	3	1	1	1	1	1	1	0	2	1	1	2	0	1	1	0	2	2	3	1
ϕ_3,6'	3	3	3	3	3	3	3	3	3	3	3	3	1	3	0	1	3	1	0	3	2	1	3	0	1	3	1	0	3	1	1	1	1	1	0	1	1	2	2	1	1	0	2	3	1	1	0	2
ϕ_3,12''	3	3	3	3	3	3	3	3	3	3	3	3	1	3	1	1	3	0	2	3	0	0	3	1	1	3	1	1	3	0	1	1	1	1	2	1	1	0	0	1	1	2	1	0	2	2	3	1
ϕ_3,6''	3	3	3	3	3	3	3	3	3	3	3	3	1	3	1	0	3	1	0	3	1	2	3	0	1	3	0	1	3	1	1	1	1	1	1	2	0	1	1	0	2	1	2	3	1	1	0	2
ϕ_4,9	4	4	4	4	4	4	4	4	4	4	4	4	0	4	2	2	4	0	1	4	1	1	4	1	2	4	0	0	4	2	0	2	0	2	2	1	2	1	2	1	2	1	1	2	1	3	2	3
ϕ_4,11	4	4	4	4	4	4	4	4	4	4	4	4	0	4	2	2	4	0	2	4	0	0	4	2	1	4	1	1	4	1	1	2	1	2	2	0	2	0	1	2	1	2	1	1	2	3	3	2
ϕ_4,7	4	4	4	4	4	4	4	4	4	4	4	4	1	4	1	1	4	1	0	4	2	2	4	0	2	4	0	0	4	2	1	2	1	2	1	2	1	2	2	0	2	0	2	3	1	2	1	3
ϕ_4,3	4	4	4	4	4	4	4	4	4	4	4	4	2	4	0	0	4	2	1	4	1	1	4	1	0	4	2	2	4	0	2	0	2	0	1	2	1	2	1	2	1	2	3	2	3	1	2	1
ϕ_4,5	4	4	4	4	4	4	4	4	4	4	4	4	2	4	0	0	4	2	0	4	2	2	4	0	1	4	1	1	4	1	2	1	2	1	0	2	0	2	2	1	2	1	3	3	2	1	1	2
ϕ_4,13	4	4	4	4	4	4	4	4	4	4	4	4	1	4	1	1	4	1	2	4	0	0	4	2	0	4	2	2	4	0	2	1	2	1	2	1	2	1	0	2	0	2	2	1	3	2	3	1

Graded characters of the simple modules

L(ϕ_1,0)

L(ϕ_1,6)

L(ϕ_1,8)

L(ϕ_1,14)

L(ϕ_1,16)

L(ϕ_1,22)

L(ϕ_1,12)

L(ϕ_1,18)

L(ϕ_1,20)

L(ϕ_1,26)

L(ϕ_1,28)

L(ϕ_1,34)

L(ϕ_2,9)

L(ϕ_2,12)

L(ϕ_2,15')

L(ϕ_2,15'')

L(ϕ_2,18)

L(ϕ_2,21)

L(ϕ_2,5)

L(ϕ_2,8)

L(ϕ_2,11')

L(ϕ_2,11'')

L(ϕ_2,14)

L(ϕ_2,17)

L(ϕ_2,1)

L(ϕ_2,4)

L(ϕ_2,7')

L(ϕ_2,7'')

L(ϕ_2,10)

L(ϕ_2,13)

L(ϕ_3,8')

L(ϕ_3,2)

L(ϕ_3,8'')

L(ϕ_3,14)

L(ϕ_3,4)

L(ϕ_3,10'')

L(ϕ_3,16)

L(ϕ_3,10')

L(ϕ_3,12')

L(ϕ_3,6')

L(ϕ_3,12'')

L(ϕ_3,6'')

L(ϕ_4,9)

L(ϕ_4,11)

L(ϕ_4,7)

L(ϕ_4,3)

L(ϕ_4,5)

L(ϕ_4,13)

ϕ_1,0

t⁶

t⁸

t¹⁴

t¹⁶

t²²

t¹²

t¹⁸

t²⁰

t²⁶

t²⁸

t³⁴

t⁹

t¹²

t¹⁸

t⁵

t⁸

t¹⁴

t⁴

t¹⁰

t²

t⁸

t⁴

t⁶

t⁷

t³

t⁵

ϕ_1,6

t⁶

t¹⁴

t⁸

t²²

t¹⁶

t¹⁸

t¹²

t²⁶

t²⁰

t³⁴

t²⁸

t¹⁸

t⁹

t¹²

t¹⁴

t⁵

t⁸

t¹⁰

t⁴

t²

t⁸

t⁴

t⁶

t³

t⁵

t⁷

ϕ_1,8

t¹⁶

t²²

t⁶

t⁸

t¹⁴

t²⁸

t³⁴

t¹²

t¹⁸

t²⁰

t²⁶

t⁴

t¹⁰

t¹²

t¹⁸

t⁹

t⁸

t¹⁴

t⁵

t⁶

t²

t⁸

t⁴

t³

t⁷

t⁵

ϕ_1,14

t²²

t¹⁶

t⁶

t¹⁴

t⁸

t³⁴

t²⁸

t¹⁸

t¹²

t²⁶

t²⁰

t¹⁰

t⁴

t¹⁸

t⁹

t¹²

t¹⁴

t⁵

t⁸

t⁶

t²

t⁸

t⁴

t⁷

t⁵

t³

ϕ_1,16

t⁸

t¹⁴

t¹⁶

t²²

t⁶

t²⁰

t²⁶

t²⁸

t³⁴

t¹²

t¹⁸

t⁸

t¹⁴

t⁵

t⁴

t¹⁰

t⁹

t¹²

t¹⁸

t⁴

t⁶

t²

t⁸

t⁵

t⁷

t³

ϕ_1,22

t¹⁴

t⁸

t²²

t¹⁶

t⁶

t²⁶

t²⁰

t³⁴

t²⁸

t¹⁸

t¹²

t¹⁴

t⁵

t⁸

t¹⁰

t⁴

t¹⁸

t⁹

t¹²

t⁴

t⁶

t²

t⁸

t⁵

t⁷

t³

ϕ_1,12

t¹²

t¹⁸

t²⁰

t²⁶

t²⁸

t³⁴

t⁶

t⁸

t¹⁴

t¹⁶

t²²

t¹²

t¹⁸

t⁹

t⁸

t¹⁴

t⁵

t⁴

t¹⁰

t⁸

t²

t⁴

t⁶

t⁷

t³

t⁵

ϕ_1,18

t¹⁸

t¹²

t²⁶

t²⁰

t³⁴

t²⁸

t⁶

t¹⁴

t⁸

t²²

t¹⁶

t¹⁸

t⁹

t¹²

t¹⁴

t⁵

t⁸

t¹⁰

t⁴

t⁸

t²

t⁴

t⁶

t³

t⁵

t⁷

ϕ_1,20

t²⁸

t³⁴

t¹²

t¹⁸

t²⁰

t²⁶

t¹⁶

t²²

t⁶

t⁸

t¹⁴

t⁴

t¹⁰

t⁹

t¹²

t¹⁸

t⁵

t⁸

t¹⁴

t⁶

t⁸

t²

t⁴

t³

t⁷

t⁵

ϕ_1,26

t³⁴

t²⁸

t¹⁸

t¹²

t²⁶

t²⁰

t²²

t¹⁶

t⁶

t¹⁴

t⁸

t¹⁰

t⁴

t¹⁸

t⁹

t¹²

t¹⁴

t⁵

t⁸

t⁶

t⁸

t²

t⁴

t⁷

t⁵

t³

ϕ_1,28

t²⁰

t²⁶

t²⁸

t³⁴

t¹²

t¹⁸

t⁸

t¹⁴

t¹⁶

t²²

t⁶

t⁵

t⁸

t¹⁴

t⁴

t¹⁰

t¹²

t¹⁸

t⁹

t⁴

t⁶

t⁸

t²

t⁵

t⁷

t³

ϕ_1,34

t²⁶

t²⁰

t³⁴

t²⁸

t¹⁸

t¹²

t¹⁴

t⁸

t²²

t¹⁶

t⁶

t¹⁴

t⁵

t⁸

t¹⁰

t⁴

t¹⁸

t⁹

t¹²

t⁴

t⁶

t⁸

t²

t⁵

t⁷

t³

ϕ_2,9

t¹⁵ + t²⁷

2t²¹

t¹¹ + t²³

t⁵ + t²⁹

t⁷ + t¹⁹

2t¹³

t¹⁵ + t²⁷

t⁹ + t³³

t¹¹ + t²³

2t¹⁷

t⁷ + t¹⁹

t + t²⁵

t³ + t¹⁵

t⁶

2t⁹

2t¹¹

t²

t⁵ + t¹⁷

t⁸

t⁷ + t¹⁹

t¹⁰

2t¹³

t⁴

2t⁵

t⁷

t³

t⁹

t³

t²

2t⁶

t⁸

2t⁴

ϕ_2,12

t¹² + t²⁴

t¹⁸ + t³⁰

t⁸ + t²⁰

t¹⁴ + t²⁶

t⁴ + t¹⁶

t¹⁰ + t²²

t¹² + t²⁴

t¹⁸ + t³⁰

t⁸ + t²⁰

t¹⁴ + t²⁶

t⁴ + t¹⁶

t¹⁰ + t²²

1 + t¹²

t³

t⁶ + t¹⁸

t⁵

2t⁸

2t¹⁴

t⁵

t⁴ + t¹⁶

t⁷

t¹⁰ + t²²

t⁸

t²

t⁸

t²

t⁴

t⁶

t⁹

t⁷

t³

2t⁵

ϕ_2,15'

2t²¹

t¹⁵ + t²⁷

t⁵ + t²⁹

t¹¹ + t²³

2t¹³

t⁷ + t¹⁹

t⁹ + t³³

t¹⁵ + t²⁷

2t¹⁷

t¹¹ + t²³

t + t²⁵

t⁷ + t¹⁹

t⁶

2t⁹

t³ + t¹⁵

t²

t⁵ + t¹⁷

t⁸

2t¹¹

2t¹³

t⁴

t⁷ + t¹⁹

t¹⁰

2t⁵

t⁷

t⁹

t³

2t⁶

t⁸

2t⁴

t²

ϕ_2,15''

t⁹ + t³³

t¹⁵ + t²⁷

2t¹⁷

t¹¹ + t²³

t + t²⁵

t⁷ + t¹⁹

2t²¹

t¹⁵ + t²⁷

t⁵ + t²⁹

t¹¹ + t²³

2t¹³

t⁷ + t¹⁹

2t⁹

t³ + t¹⁵

t⁶

t⁵ + t¹⁷

t⁸

2t¹¹

t²

t¹⁰

2t¹³

t⁴

t⁷ + t¹⁹

2t⁵

t⁷

t³

t⁹

t³

2t⁶

t⁸

2t⁴

t²

ϕ_2,18

t¹⁸ + t³⁰

t¹² + t²⁴

t¹⁴ + t²⁶

t⁸ + t²⁰

t¹⁰ + t²²

t⁴ + t¹⁶

t¹⁸ + t³⁰

t¹² + t²⁴

t¹⁴ + t²⁶

t⁸ + t²⁰

t¹⁰ + t²²

t⁴ + t¹⁶

t³

t⁶ + t¹⁸

1 + t¹²

t³

2t¹⁴

t⁵

2t⁸

t⁷

t¹⁰ + t²²

t⁴ + t¹⁶

t⁷

t²

t⁸

t²

t⁸

t⁴

t⁶

t³

2t⁵

t⁹

t⁷

ϕ_2,21

t¹⁵ + t²⁷

t⁹ + t³³

t¹¹ + t²³

2t¹⁷

t⁷ + t¹⁹

t + t²⁵

t¹⁵ + t²⁷

2t²¹

t¹¹ + t²³

t⁵ + t²⁹

t⁷ + t¹⁹

2t¹³

t³ + t¹⁵

t⁶

2t⁹

t⁸

2t¹¹

t²

t⁵ + t¹⁷

t⁴

t⁷ + t¹⁹

t¹⁰

2t¹³

2t⁵

t⁷

t³

t⁹

t²

2t⁶

t⁸

2t⁴

ϕ_2,5

t⁷ + t¹⁹

t + t²⁵

t¹⁵ + t²⁷

t⁹ + t³³

t¹¹ + t²³

2t¹⁷

t⁷ + t¹⁹

2t¹³

t¹⁵ + t²⁷

2t²¹

t¹¹ + t²³

t⁵ + t²⁹

t⁴

t⁷ + t¹⁹

t¹⁰

2t¹³

t³ + t¹⁵

t⁶

2t⁹

2t¹¹

t²

t⁵ + t¹⁷

t⁸

t³

t⁹

2t⁵

t⁷

2t⁴

2t⁶

t²

t⁸

ϕ_2,8

t⁴ + t¹⁶

t¹⁰ + t²²

t¹² + t²⁴

t¹⁸ + t³⁰

t⁸ + t²⁰

t¹⁴ + t²⁶

t⁴ + t¹⁶

t¹⁰ + t²²

t¹² + t²⁴

t¹⁸ + t³⁰

t⁸ + t²⁰

t¹⁴ + t²⁶

t⁴ + t¹⁶

t⁷

t¹⁰ + t²²

1 + t¹²

t³

t⁶ + t¹⁸

t⁵

2t⁸

2t¹⁴

t⁵

t⁶

t⁸

t²

t⁸

t²

t⁴

t³

t⁷

t⁹

2t⁵

ϕ_2,11'

2t¹³

t⁷ + t¹⁹

2t²¹

t¹⁵ + t²⁷

t⁵ + t²⁹

t¹¹ + t²³

t + t²⁵

t⁷ + t¹⁹

t⁹ + t³³

t¹⁵ + t²⁷

2t¹⁷

t¹¹ + t²³

2t¹³

t⁴

t⁷ + t¹⁹

t¹⁰

2t⁹

t³ + t¹⁵

t⁶

t⁵ + t¹⁷

t⁸

2t¹¹

t²

t⁹

t³

2t⁵

t⁷

t⁸

2t⁴

2t⁶

t²

ϕ_2,11''

t + t²⁵

t⁷ + t¹⁹

t⁹ + t³³

t¹⁵ + t²⁷

2t¹⁷

t¹¹ + t²³

2t¹³

t⁷ + t¹⁹

2t²¹

t¹⁵ + t²⁷

t⁵ + t²⁹

t¹¹ + t²³

t¹⁰

2t¹³

t⁴

t⁷ + t¹⁹

t⁶

2t⁹

t³ + t¹⁵

t²

t⁵ + t¹⁷

t⁸

2t¹¹

t³

t⁹

t³

2t⁵

t⁷

t⁸

2t⁴

2t⁶

t²

ϕ_2,14

t¹⁰ + t²²

t⁴ + t¹⁶

t¹⁸ + t³⁰

t¹² + t²⁴

t¹⁴ + t²⁶

t⁸ + t²⁰

t¹⁰ + t²²

t⁴ + t¹⁶

t¹⁸ + t³⁰

t¹² + t²⁴

t¹⁴ + t²⁶

t⁸ + t²⁰

t⁷

t¹⁰ + t²²

t⁴ + t¹⁶

t⁷

t³

t⁶ + t¹⁸

1 + t¹²

t³

2t¹⁴

t⁵

2t⁸

t⁶

t²

t⁸

t²

t⁸

t⁴

t⁷

t⁹

2t⁵

t³

ϕ_2,17

t⁷ + t¹⁹

2t¹³

t¹⁵ + t²⁷

2t²¹

t¹¹ + t²³

t⁵ + t²⁹

t⁷ + t¹⁹

t + t²⁵

t¹⁵ + t²⁷

t⁹ + t³³

t¹¹ + t²³

2t¹⁷

t⁷ + t¹⁹

t¹⁰

2t¹³

t⁴

t³ + t¹⁵

t⁶

2t⁹

t⁸

2t¹¹

t²

t⁵ + t¹⁷

t³

t⁹

t³

2t⁵

t⁷

2t⁴

2t⁶

t²

t⁸

ϕ_2,1

t¹¹ + t²³

t⁵ + t²⁹

t⁷ + t¹⁹

2t¹³

t¹⁵ + t²⁷

2t²¹

t¹¹ + t²³

2t¹⁷

t⁷ + t¹⁹

t + t²⁵

t¹⁵ + t²⁷

t⁹ + t³³

t⁸

2t¹¹

t²

t⁵ + t¹⁷

t⁴

t⁷ + t¹⁹

t¹⁰

2t¹³

t³ + t¹⁵

t⁶

2t⁹

t⁷

t³

t⁹

t³

2t⁵

t⁸

2t⁶

t²

2t⁴

ϕ_2,4

t⁸ + t²⁰

t¹⁴ + t²⁶

t⁴ + t¹⁶

t¹⁰ + t²²

t¹² + t²⁴

t¹⁸ + t³⁰

t⁸ + t²⁰

t¹⁴ + t²⁶

t⁴ + t¹⁶

t¹⁰ + t²²

t¹² + t²⁴

t¹⁸ + t³⁰

t⁵

2t⁸

2t¹⁴

t⁵

t⁴ + t¹⁶

t⁷

t¹⁰ + t²²

1 + t¹²

t³

t⁶ + t¹⁸

t⁴

t⁶

t⁸

t²

t⁸

t²

2t⁵

t⁷

t³

t⁹

ϕ_2,7'

2t¹⁷

t¹¹ + t²³

t + t²⁵

t⁷ + t¹⁹

t⁹ + t³³

t¹⁵ + t²⁷

t⁵ + t²⁹

t¹¹ + t²³

2t¹³

t⁷ + t¹⁹

2t²¹

t¹⁵ + t²⁷

t²

t⁵ + t¹⁷

t⁸

2t¹¹

2t¹³

t⁴

t⁷ + t¹⁹

t¹⁰

2t⁹

t³ + t¹⁵

t⁶

t⁷

t³

t⁹

t³

2t⁵

t²

2t⁴

t⁸

2t⁶

ϕ_2,7''

t⁵ + t²⁹

t¹¹ + t²³

2t¹³

t⁷ + t¹⁹

2t²¹

t¹⁵ + t²⁷

2t¹⁷

t¹¹ + t²³

t + t²⁵

t⁷ + t¹⁹

t⁹ + t³³

t¹⁵ + t²⁷

t⁵ + t¹⁷

t⁸

2t¹¹

t²

t¹⁰

2t¹³

t⁴

t⁷ + t¹⁹

t⁶

2t⁹

t³ + t¹⁵

t⁷

t⁹

t³

2t⁵

t²

2t⁴

t⁸

2t⁶

ϕ_2,10

t¹⁴ + t²⁶

t⁸ + t²⁰

t¹⁰ + t²²

t⁴ + t¹⁶

t¹⁸ + t³⁰

t¹² + t²⁴

t¹⁴ + t²⁶

t⁸ + t²⁰

t¹⁰ + t²²

t⁴ + t¹⁶

t¹⁸ + t³⁰

t¹² + t²⁴

2t¹⁴

t⁵

2t⁸

t⁷

t¹⁰ + t²²

t⁴ + t¹⁶

t⁷

t³

t⁶ + t¹⁸

1 + t¹²

t³

t⁴

t⁶

t²

t⁸

t²

t⁸

t⁹

2t⁵

t⁷

t³

ϕ_2,13

t¹¹ + t²³

2t¹⁷

t⁷ + t¹⁹

t + t²⁵

t¹⁵ + t²⁷

t⁹ + t³³

t¹¹ + t²³

t⁵ + t²⁹

t⁷ + t¹⁹

2t¹³

t¹⁵ + t²⁷

2t²¹

2t¹¹

t²

t⁵ + t¹⁷

t⁸

t⁷ + t¹⁹

t¹⁰

2t¹³

t⁴

t³ + t¹⁵

t⁶

2t⁹

t⁷

t³

t⁹

2t⁵

t⁸

2t⁶

t²

2t⁴

ϕ_3,8'

t⁴ + t¹⁶ + t²⁸

2t¹⁰ + t²²

2t¹² + t²⁴

t⁶ + 2t¹⁸

t⁸ + 2t²⁰

t² + t¹⁴ + t²⁶

2t¹⁶ + t²⁸

t¹⁰ + 2t²²

t¹² + 2t²⁴

t⁶ + t¹⁸ + t³⁰

t⁸ + t²⁰ + t³²

2t¹⁴ + t²⁶

t⁴ + 2t¹⁶

t⁷

3t¹⁰

t⁹

3t¹²

t³

2t⁶ + t¹⁸

2t⁵

2t⁸ + t²⁰

t² + 2t¹⁴

t⁵

2t⁶

t⁶

t⁸

t²

t⁸

t²

t⁴

2t⁴

t¹⁰

2t³

2t⁷

t⁹

3t⁵

ϕ_3,2

2t¹⁰ + t²²

t⁴ + t¹⁶ + t²⁸

t⁶ + 2t¹⁸

2t¹² + t²⁴

t² + t¹⁴ + t²⁶

t⁸ + 2t²⁰

t¹⁰ + 2t²²

2t¹⁶ + t²⁸

t⁶ + t¹⁸ + t³⁰

t¹² + 2t²⁴

2t¹⁴ + t²⁶

t⁸ + t²⁰ + t³²

t⁷

3t¹⁰

t⁴ + 2t¹⁶

t⁷

t³

2t⁶ + t¹⁸

t⁹

3t¹²

t³

t² + 2t¹⁴

t⁵

2t⁵

2t⁸ + t²⁰

2t⁶

t⁶

t²

t⁸

t²

t⁸

t⁴

t¹⁰

2t⁴

2t⁷

t⁹

3t⁵

2t³

ϕ_3,8''

2t¹⁶ + t²⁸

t¹⁰ + 2t²²

t¹² + 2t²⁴

t⁶ + t¹⁸ + t³⁰

t⁸ + t²⁰ + t³²

2t¹⁴ + t²⁶

t⁴ + t¹⁶ + t²⁸

2t¹⁰ + t²²

2t¹² + t²⁴

t⁶ + 2t¹⁸

t⁸ + 2t²⁰

t² + t¹⁴ + t²⁶

t⁴ + 2t¹⁶

t⁷

3t¹⁰

3t¹²

t³

2t⁶ + t¹⁸

t⁹

t⁵

2t⁸ + t²⁰

t² + 2t¹⁴

2t⁵

t⁶

2t⁶

t⁸

t²

t⁸

t²

2t⁴

t¹⁰

t⁴

2t³

2t⁷

t⁹

3t⁵

ϕ_3,14

t¹⁰ + 2t²²

2t¹⁶ + t²⁸

t⁶ + t¹⁸ + t³⁰

t¹² + 2t²⁴

2t¹⁴ + t²⁶

t⁸ + t²⁰ + t³²

2t¹⁰ + t²²

t⁴ + t¹⁶ + t²⁸

t⁶ + 2t¹⁸

2t¹² + t²⁴

t² + t¹⁴ + t²⁶

t⁸ + 2t²⁰

t⁷

3t¹⁰

t⁴ + 2t¹⁶

t⁷

t³

2t⁶ + t¹⁸

t⁹

3t¹²

t³

t² + 2t¹⁴

2t⁵

t⁵

2t⁸ + t²⁰

t⁶

2t⁶

t²

t⁸

t²

t⁸

t¹⁰

2t⁴

t⁴

2t⁷

t⁹

3t⁵

2t³

ϕ_3,4

t⁸ + 2t²⁰

t² + t¹⁴ + t²⁶

t⁴ + t¹⁶ + t²⁸

2t¹⁰ + t²²

2t¹² + t²⁴

t⁶ + 2t¹⁸

t⁸ + t²⁰ + t³²

2t¹⁴ + t²⁶

2t¹⁶ + t²⁸

t¹⁰ + 2t²²

t¹² + 2t²⁴

t⁶ + t¹⁸ + t³⁰

2t⁵

2t⁸ + t²⁰

t² + 2t¹⁴

t⁵

t⁴ + 2t¹⁶

t⁷

3t¹⁰

3t¹²

t³

2t⁶ + t¹⁸

t⁹

t⁴

2t⁴

t¹⁰

2t⁶

t⁶

t⁸

t²

t⁸

t²

3t⁵

2t⁷

2t³

t⁹

ϕ_3,10''

t² + t¹⁴ + t²⁶

t⁸ + 2t²⁰

2t¹⁰ + t²²

t⁴ + t¹⁶ + t²⁸

t⁶ + 2t¹⁸

2t¹² + t²⁴

2t¹⁴ + t²⁶

t⁸ + t²⁰ + t³²

t¹⁰ + 2t²²

2t¹⁶ + t²⁸

t⁶ + t¹⁸ + t³⁰

t¹² + 2t²⁴

t² + 2t¹⁴

2t⁵

t⁵

2t⁸ + t²⁰

t⁷

3t¹⁰

t⁴ + 2t¹⁶

t⁷

t³

2t⁶ + t¹⁸

t⁹

3t¹²

t³

t⁴

t¹⁰

2t⁴

2t⁶

t⁶

t²

t⁸

t²

t⁸

t⁹

3t⁵

2t⁷

2t³

ϕ_3,16

t⁸ + t²⁰ + t³²

2t¹⁴ + t²⁶

2t¹⁶ + t²⁸

t¹⁰ + 2t²²

t¹² + 2t²⁴

t⁶ + t¹⁸ + t³⁰

t⁸ + 2t²⁰

t² + t¹⁴ + t²⁶

t⁴ + t¹⁶ + t²⁸

2t¹⁰ + t²²

2t¹² + t²⁴

t⁶ + 2t¹⁸

t⁵

2t⁸ + t²⁰

t² + 2t¹⁴

2t⁵

t⁴ + 2t¹⁶

t⁷

3t¹⁰

t⁹

3t¹²

t³

2t⁶ + t¹⁸

2t⁴

t¹⁰

t⁴

t⁶

2t⁶

t⁸

t²

t⁸

t²

3t⁵

2t⁷

2t³

t⁹

ϕ_3,10'

2t¹⁴ + t²⁶

t⁸ + t²⁰ + t³²

t¹⁰ + 2t²²

2t¹⁶ + t²⁸

t⁶ + t¹⁸ + t³⁰

t¹² + 2t²⁴

t² + t¹⁴ + t²⁶

t⁸ + 2t²⁰

2t¹⁰ + t²²

t⁴ + t¹⁶ + t²⁸

t⁶ + 2t¹⁸

2t¹² + t²⁴

t² + 2t¹⁴

t⁵

2t⁵

2t⁸ + t²⁰

t⁷

3t¹⁰

t⁴ + 2t¹⁶

t⁷

t³

2t⁶ + t¹⁸

t⁹

3t¹²

t³

t¹⁰

2t⁴

t⁴

t⁶

2t⁶

t²

t⁸

t²

t⁸

t⁹

3t⁵

2t⁷

2t³

ϕ_3,12'

2t¹² + t²⁴

t⁶ + 2t¹⁸

t⁸ + 2t²⁰

t² + t¹⁴ + t²⁶

t⁴ + t¹⁶ + t²⁸

2t¹⁰ + t²²

t¹² + 2t²⁴

t⁶ + t¹⁸ + t³⁰

t⁸ + t²⁰ + t³²

2t¹⁴ + t²⁶

2t¹⁶ + t²⁸

t¹⁰ + 2t²²

3t¹²

t³

2t⁶ + t¹⁸

t⁹

t⁵

2t⁸ + t²⁰

t² + 2t¹⁴

2t⁵

t⁴ + 2t¹⁶

t⁷

3t¹⁰

t⁸

t²

t⁸

t²

t⁴

2t⁴

t¹⁰

2t⁶

t⁶

t⁹

2t⁷

2t³

3t⁵

ϕ_3,6'

t⁶ + 2t¹⁸

2t¹² + t²⁴

t² + t¹⁴ + t²⁶

t⁸ + 2t²⁰

2t¹⁰ + t²²

t⁴ + t¹⁶ + t²⁸

t⁶ + t¹⁸ + t³⁰

t¹² + 2t²⁴

2t¹⁴ + t²⁶

t⁸ + t²⁰ + t³²

t¹⁰ + 2t²²

2t¹⁶ + t²⁸

t³

2t⁶ + t¹⁸

t⁹

3t¹²

t³

t² + 2t¹⁴

2t⁵

t⁵

2t⁸ + t²⁰

t⁷

3t¹⁰

t⁴ + 2t¹⁶

t⁷

t²

t⁸

t²

t⁸

t⁴

t¹⁰

2t⁴

2t⁶

t⁶

2t³

3t⁵

t⁹

2t⁷

ϕ_3,12''

t¹² + 2t²⁴

t⁶ + t¹⁸ + t³⁰

t⁸ + t²⁰ + t³²

2t¹⁴ + t²⁶

2t¹⁶ + t²⁸

t¹⁰ + 2t²²

2t¹² + t²⁴

t⁶ + 2t¹⁸

t⁸ + 2t²⁰

t² + t¹⁴ + t²⁶

t⁴ + t¹⁶ + t²⁸

2t¹⁰ + t²²

t⁹

3t¹²

t³

2t⁶ + t¹⁸

2t⁵

2t⁸ + t²⁰

t² + 2t¹⁴

t⁵

t⁴ + 2t¹⁶

t⁷

3t¹⁰

t⁸

t²

t⁸

t²

2t⁴

t¹⁰

t⁴

t⁶

2t⁶

t⁹

2t⁷

2t³

3t⁵

ϕ_3,6''

t⁶ + t¹⁸ + t³⁰

t¹² + 2t²⁴

2t¹⁴ + t²⁶

t⁸ + t²⁰ + t³²

t¹⁰ + 2t²²

2t¹⁶ + t²⁸

t⁶ + 2t¹⁸

2t¹² + t²⁴

t² + t¹⁴ + t²⁶

t⁸ + 2t²⁰

2t¹⁰ + t²²

t⁴ + t¹⁶ + t²⁸

t³

2t⁶ + t¹⁸

t⁹

3t¹²

t³

t² + 2t¹⁴

t⁵

2t⁵

2t⁸ + t²⁰

t⁷

3t¹⁰

t⁴ + 2t¹⁶

t⁷

t²

t⁸

t²

t⁸

t¹⁰

2t⁴

t⁴

t⁶

2t⁶

2t³

3t⁵

t⁹

2t⁷

ϕ_4,9

t³ + 2t¹⁵ + t²⁷

2t⁹ + 2t²¹

2t¹¹ + 2t²³

t⁵ + 2t¹⁷ + t²⁹

t⁷ + 2t¹⁹ + t³¹

2t¹³ + 2t²⁵

t³ + 2t¹⁵ + t²⁷

2t⁹ + 2t²¹

2t¹¹ + 2t²³

t⁵ + 2t¹⁷ + t²⁹

t⁷ + 2t¹⁹ + t³¹

2t¹³ + 2t²⁵

t³ + 3t¹⁵

2t⁶

3t⁹ + t²¹

t⁸

4t¹¹

t²

2t⁵ + 2t¹⁷

t⁸

2t⁴

3t⁷ + t¹⁹

t + 3t¹³

2t⁴

2t⁵

2t⁷

2t³

t⁹

2t³

t⁹

2t²

t¹⁰

3t⁶

2t⁸

3t⁴

ϕ_4,11

2t¹³ + 2t²⁵

t⁷ + 2t¹⁹ + t³¹

2t⁹ + 2t²¹

t³ + 2t¹⁵ + t²⁷

t⁵ + 2t¹⁷ + t²⁹

2t¹¹ + 2t²³

2t¹³ + 2t²⁵

t⁷ + 2t¹⁹ + t³¹

2t⁹ + 2t²¹

t³ + 2t¹⁵ + t²⁷

t⁵ + 2t¹⁷ + t²⁹

2t¹¹ + 2t²³

t + 3t¹³

2t⁴

3t⁷ + t¹⁹

2t⁶

3t⁹ + t²¹

t³ + 3t¹⁵

2t⁶

t²

2t⁵ + 2t¹⁷

t⁸

4t¹¹

t²

t⁹

2t³

t⁹

2t³

2t⁵

2t⁷

t¹⁰

2t⁸

3t⁴

3t⁶

2t²

ϕ_4,7

t⁵ + 2t¹⁷ + t²⁹

2t¹¹ + 2t²³

2t¹³ + 2t²⁵

t⁷ + 2t¹⁹ + t³¹

2t⁹ + 2t²¹

t³ + 2t¹⁵ + t²⁷

t⁵ + 2t¹⁷ + t²⁹

2t¹¹ + 2t²³

2t¹³ + 2t²⁵

t⁷ + 2t¹⁹ + t³¹

2t⁹ + 2t²¹

t³ + 2t¹⁵ + t²⁷

t²

2t⁵ + 2t¹⁷

t⁸

4t¹¹

t²

t + 3t¹³

2t⁴

3t⁷ + t¹⁹

2t⁶

3t⁹ + t²¹

t³ + 3t¹⁵

2t⁶

2t⁷

t⁹

2t³

t⁹

2t³

2t⁵

2t²

3t⁴

2t⁸

t¹⁰

3t⁶

ϕ_4,3

2t⁹ + 2t²¹

t³ + 2t¹⁵ + t²⁷

t⁵ + 2t¹⁷ + t²⁹

2t¹¹ + 2t²³

2t¹³ + 2t²⁵

t⁷ + 2t¹⁹ + t³¹

2t⁹ + 2t²¹

t³ + 2t¹⁵ + t²⁷

t⁵ + 2t¹⁷ + t²⁹

2t¹¹ + 2t²³

2t¹³ + 2t²⁵

t⁷ + 2t¹⁹ + t³¹

2t⁶

3t⁹ + t²¹

t³ + 3t¹⁵

2t⁶

t²

2t⁵ + 2t¹⁷

t⁸

4t¹¹

t²

t + 3t¹³

2t⁴

3t⁷ + t¹⁹

2t⁵

2t⁷

t⁹

2t³

t⁹

2t³

3t⁶

2t⁸

3t⁴

2t²

t¹⁰

ϕ_4,5

t⁷ + 2t¹⁹ + t³¹

2t¹³ + 2t²⁵

t³ + 2t¹⁵ + t²⁷

2t⁹ + 2t²¹

2t¹¹ + 2t²³

t⁵ + 2t¹⁷ + t²⁹

t⁷ + 2t¹⁹ + t³¹

2t¹³ + 2t²⁵

t³ + 2t¹⁵ + t²⁷

2t⁹ + 2t²¹

2t¹¹ + 2t²³

t⁵ + 2t¹⁷ + t²⁹

2t⁴

3t⁷ + t¹⁹

t + 3t¹³

2t⁴

t³ + 3t¹⁵

2t⁶

3t⁹ + t²¹

t⁸

4t¹¹

t²

2t⁵ + 2t¹⁷

t⁸

2t³

t⁹

2t³

t⁹

2t⁵

2t⁷

3t⁴

3t⁶

2t²

t¹⁰

2t⁸

ϕ_4,13

2t¹¹ + 2t²³

t⁵ + 2t¹⁷ + t²⁹

t⁷ + 2t¹⁹ + t³¹

2t¹³ + 2t²⁵

t³ + 2t¹⁵ + t²⁷

2t⁹ + 2t²¹

2t¹¹ + 2t²³

t⁵ + 2t¹⁷ + t²⁹

t⁷ + 2t¹⁹ + t³¹

2t¹³ + 2t²⁵

t³ + 2t¹⁵ + t²⁷

2t⁹ + 2t²¹

t⁸

4t¹¹

t²

2t⁵ + 2t¹⁷

t⁸

2t⁴

3t⁷ + t¹⁹

t + 3t¹³

2t⁴

t³ + 3t¹⁵

2t⁶

3t⁹ + t²¹

2t⁷

2t³

t⁹

2t³

t⁹

2t⁵

2t⁸

t¹⁰

3t⁶

2t²

3t⁴

Exceptional hyperplanes

Unknown

The representation theory of the restricted rational Cherednik algebra for G15

For generic parameters

Non-singleton Calogero–Moser families

Dimensions, Poincaré series and diagonal Verma multiplicities of the simple modules

Characters of the simple modules

Graded characters of the simple modules

Exceptional hyperplanes

The representation theory of the restricted rational Cherednik algebra for G₁₅