The representation theory of the restricted rational Cherednik algebra for G₇

Computed by Ulrich Thiel using CHAMP (see LMS J. Comput. Math., 2015). Last update on Fri Mar 27 12:48:14 CET 2015.

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

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For generic parameters

Non-singleton Calogero–Moser families

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

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	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,4'	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,8'	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,4''	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,8''	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,12'	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,8'''	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,12''	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,16	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,6	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,10'	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,14'	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,10''	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,14''	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,18'	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,14'''	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,18''	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_1,22	144	1	1 + 2t + 3t² + 4t³ + 5t⁴ + 6t⁵ + 7t⁶ + 8t⁷ + 9t⁸ + 10t⁹ + 11t¹⁰ + 12t¹¹ + 11t¹² + 10t¹³ + 9t¹⁴ + 8t¹⁵ + 7t¹⁶ + 6t¹⁷ + 5t¹⁸ + 4t¹⁹ + 3t²⁰ + 2t²¹ + t²²
ϕ_2,9'	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_2,11'	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_2,11''	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,9''	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_2,9'''	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_2,15	72	2	2 + 4t + 6t² + 8t³ + 10t⁴ + 12t⁵ + 10t⁶ + 8t⁷ + 6t⁸ + 4t⁹ + 2t¹⁰
ϕ_2,13'	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_2,13''	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_2,3'	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_2,3''	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_3,10	48	3	3 + 6t + 9t² + 12t³ + 9t⁴ + 6t⁵ + 3t⁶
ϕ_3,4	48	3	3 + 6t + 9t² + 12t³ + 9t⁴ + 6t⁵ + 3t⁶
ϕ_3,2	48	3	3 + 6t + 9t² + 12t³ + 9t⁴ + 6t⁵ + 3t⁶
ϕ_3,8	48	3	3 + 6t + 9t² + 12t³ + 9t⁴ + 6t⁵ + 3t⁶
ϕ_3,6	48	3	3 + 6t + 9t² + 12t³ + 9t⁴ + 6t⁵ + 3t⁶
ϕ_3,12	48	3	3 + 6t + 9t² + 12t³ + 9t⁴ + 6t⁵ + 3t⁶

Characters of the simple modules

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

Graded characters of the simple modules

L(ϕ_1,0)

L(ϕ_1,4')

L(ϕ_1,8')

L(ϕ_1,4'')

L(ϕ_1,8'')

L(ϕ_1,12')

L(ϕ_1,8''')

L(ϕ_1,12'')

L(ϕ_1,16)

L(ϕ_1,6)

L(ϕ_1,10')

L(ϕ_1,14')

L(ϕ_1,10'')

L(ϕ_1,14'')

L(ϕ_1,18')

L(ϕ_1,14''')

L(ϕ_1,18'')

L(ϕ_1,22)

L(ϕ_2,9')

L(ϕ_2,7')

L(ϕ_2,11')

L(ϕ_2,7'')

L(ϕ_2,11'')

L(ϕ_2,9'')

L(ϕ_2,11''')

L(ϕ_2,9''')

L(ϕ_2,7''')

L(ϕ_2,15)

L(ϕ_2,13')

L(ϕ_2,5')

L(ϕ_2,13'')

L(ϕ_2,5'')

L(ϕ_2,3')

L(ϕ_2,5''')

L(ϕ_2,3'')

L(ϕ_2,1)

L(ϕ_3,10)

L(ϕ_3,4)

L(ϕ_3,2)

L(ϕ_3,8)

L(ϕ_3,6)

L(ϕ_3,12)

ϕ_1,0

t⁴

t⁸

t⁴

t⁸

t¹²

t⁸

t¹²

t¹⁶

t⁶

t¹⁰

t¹⁴

t¹⁰

t¹⁴

t¹⁸

t¹⁴

t¹⁸

t²²

t⁹

t⁷

t⁵

t³

t⁵

t³

t⁴

t²

ϕ_1,4'

t⁸

t⁴

t¹²

t⁴

t⁸

t¹⁶

t⁸

t¹²

t¹⁴

t⁶

t¹⁰

t¹⁸

t¹⁰

t¹⁴

t²²

t¹⁴

t¹⁸

t⁵

t⁷

t³

t⁷

t⁵

t³

t⁹

t⁴

t²

ϕ_1,8'

t⁴

t⁸

t¹²

t⁴

t¹²

t¹⁶

t⁸

t¹⁰

t¹⁴

t⁶

t¹⁴

t¹⁸

t¹⁰

t¹⁸

t²²

t¹⁴

t³

t⁷

t⁵

t⁹

t⁵

t⁷

t⁵

t²

t⁴

ϕ_1,4''

t⁸

t¹²

t¹⁶

t⁴

t⁸

t⁴

t⁸

t¹²

t¹⁴

t¹⁸

t²²

t⁶

t¹⁰

t¹⁴

t¹⁰

t¹⁴

t¹⁸

t⁵

t³

t⁷

t⁵

t⁷

t⁵

t³

t⁹

t⁴

t²

ϕ_1,8''

t¹⁶

t⁸

t¹²

t⁸

t⁴

t¹²

t⁴

t⁸

t²²

t¹⁴

t¹⁸

t¹⁴

t⁶

t¹⁰

t¹⁸

t¹⁰

t¹⁴

t³

t⁵

t⁹

t⁷

t⁵

t²

t⁴

ϕ_1,12'

t¹²

t¹⁶

t⁸

t⁴

t⁸

t¹²

t⁴

t¹⁸

t²²

t¹⁴

t¹⁰

t¹⁴

t⁶

t¹⁴

t¹⁸

t¹⁰

t⁷

t⁹

t⁷

t³

t⁵

t³

t⁴

t²

ϕ_1,8'''

t⁴

t⁸

t¹²

t⁸

t¹²

t¹⁶

t⁴

t⁸

t¹⁰

t¹⁴

t¹⁸

t¹⁴

t¹⁸

t²²

t⁶

t¹⁰

t¹⁴

t³

t⁷

t⁵

t⁹

t⁷

t⁵

t²

t⁴

ϕ_1,12''

t¹²

t⁴

t⁸

t¹⁶

t⁸

t¹²

t⁸

t⁴

t¹⁸

t¹⁰

t¹⁴

t²²

t¹⁴

t¹⁸

t¹⁴

t⁶

t¹⁰

t⁷

t⁹

t⁷

t³

t⁵

t³

t⁵

t⁴

t²

ϕ_1,16

t⁸

t¹²

t⁴

t¹²

t¹⁶

t⁸

t⁴

t⁸

t¹⁴

t¹⁸

t¹⁰

t¹⁸

t²²

t¹⁴

t¹⁰

t¹⁴

t⁶

t⁵

t³

t⁷

t³

t⁵

t⁷

t⁵

t⁹

t⁴

t²

ϕ_1,6

t⁶

t¹⁰

t¹⁴

t¹⁰

t¹⁴

t¹⁸

t¹⁴

t¹⁸

t²²

t⁴

t⁸

t⁴

t⁸

t¹²

t⁸

t¹²

t¹⁶

t⁵

t³

t⁵

t³

t⁹

t⁷

t⁴

t²

ϕ_1,10'

t¹⁴

t⁶

t¹⁰

t¹⁸

t¹⁰

t¹⁴

t²²

t¹⁴

t¹⁸

t⁸

t⁴

t¹²

t⁴

t⁸

t¹⁶

t⁸

t¹²

t⁹

t⁵

t⁷

t³

t⁷

t⁵

t³

t⁴

t²

ϕ_1,14'

t¹⁰

t¹⁴

t⁶

t¹⁴

t¹⁸

t¹⁰

t¹⁸

t²²

t¹⁴

t⁴

t⁸

t¹²

t⁴

t¹²

t¹⁶

t⁸

t⁷

t⁵

t⁹

t⁵

t⁷

t⁵

t³

t²

t⁴

ϕ_1,10''

t¹⁴

t¹⁸

t²²

t⁶

t¹⁰

t¹⁴

t¹⁰

t¹⁴

t¹⁸

t⁸

t¹²

t¹⁶

t⁴

t⁸

t⁴

t⁸

t¹²

t⁹

t⁵

t³

t⁷

t⁵

t⁷

t⁵

t³

t⁴

t²

ϕ_1,14''

t²²

t¹⁴

t¹⁸

t¹⁴

t⁶

t¹⁰

t¹⁸

t¹⁰

t¹⁴

t¹⁶

t⁸

t¹²

t⁸

t⁴

t¹²

t⁴

t⁸

t⁵

t⁹

t⁷

t⁵

t³

t²

t⁴

ϕ_1,18'

t¹⁸

t²²

t¹⁴

t¹⁰

t¹⁴

t⁶

t¹⁴

t¹⁸

t¹⁰

t¹²

t¹⁶

t⁸

t⁴

t⁸

t¹²

t⁴

t³

t⁵

t³

t⁷

t⁹

t⁷

t⁴

t²

ϕ_1,14'''

t¹⁰

t¹⁴

t¹⁸

t¹⁴

t¹⁸

t²²

t⁶

t¹⁰

t¹⁴

t⁴

t⁸

t¹²

t⁸

t¹²

t¹⁶

t⁴

t⁸

t⁷

t⁵

t⁹

t⁷

t⁵

t³

t²

t⁴

ϕ_1,18''

t¹⁸

t¹⁰

t¹⁴

t²²

t¹⁴

t¹⁸

t¹⁴

t⁶

t¹⁰

t¹²

t⁴

t⁸

t¹⁶

t⁸

t¹²

t⁸

t⁴

t³

t⁵

t³

t⁵

t⁷

t⁹

t⁷

t⁴

t²

ϕ_1,22

t¹⁴

t¹⁸

t¹⁰

t¹⁸

t²²

t¹⁴

t¹⁰

t¹⁴

t⁶

t⁸

t¹²

t⁴

t¹²

t¹⁶

t⁸

t⁴

t⁸

t⁹

t⁵

t³

t⁷

t³

t⁵

t⁷

t⁵

t⁴

t²

ϕ_2,9'

2t¹⁵

t⁷ + t¹⁹

2t¹¹

t⁷ + t¹⁹

2t¹¹

t³ + t¹⁵

2t¹¹

t³ + t¹⁵

2t⁷

t⁹ + t²¹

2t¹³

t⁵ + t¹⁷

2t¹³

t⁵ + t¹⁷

2t⁹

t⁵ + t¹⁷

2t⁹

t + t¹³

t²

t¹⁰

t⁶

2t⁴

t⁸

2t⁴

t⁸

2t⁶

t⁸

2t⁶

t⁴

t⁵

2t³

ϕ_2,7'

t⁵ + t¹⁷

t⁹ + t²¹

2t¹³

2t⁹

2t¹³

t⁵ + t¹⁷

t + t¹³

t⁵ + t¹⁷

2t⁹

2t¹¹

2t¹⁵

t⁷ + t¹⁹

t³ + t¹⁵

t⁷ + t¹⁹

2t¹¹

2t⁷

2t¹¹

t³ + t¹⁵

t²

2t⁴

t²

t⁴

t²

t⁸

t⁶

2t⁶

t⁸

t¹⁰

t⁸

2t⁶

2t³

t⁵

ϕ_2,11'

2t¹³

t⁵ + t¹⁷

t⁹ + t²¹

t⁵ + t¹⁷

2t⁹

2t¹³

2t⁹

t + t¹³

t⁵ + t¹⁷

t⁷ + t¹⁹

2t¹¹

2t¹⁵

2t¹¹

t³ + t¹⁵

t⁷ + t¹⁹

t³ + t¹⁵

2t⁷

2t¹¹

t⁸

t¹⁰

t⁸

2t⁴

t²

t⁶

t²

2t⁶

2t⁴

2t⁶

t⁴

t²

t⁵

2t³

ϕ_2,7''

t⁵ + t¹⁷

2t⁹

t + t¹³

t⁹ + t²¹

2t¹³

t⁵ + t¹⁷

2t¹³

t⁵ + t¹⁷

2t⁹

2t¹¹

t³ + t¹⁵

2t⁷

2t¹⁵

t⁷ + t¹⁹

2t¹¹

t⁷ + t¹⁹

2t¹¹

t³ + t¹⁵

t²

t⁴

2t⁴

t²

2t⁴

t²

t⁸

2t⁶

t¹⁰

t⁶

t⁸

2t⁶

2t³

t⁵

ϕ_2,11''

t + t¹³

t⁵ + t¹⁷

2t⁹

t⁵ + t¹⁷

t⁹ + t²¹

2t¹³

2t⁹

2t¹³

t⁵ + t¹⁷

2t⁷

2t¹¹

t³ + t¹⁵

2t¹¹

2t¹⁵

t⁷ + t¹⁹

t³ + t¹⁵

t⁷ + t¹⁹

2t¹¹

t¹⁰

t⁸

t⁴

t²

2t⁶

t²

t⁶

2t⁴

2t⁶

2t⁴

t²

t⁵

2t³

ϕ_2,9''

t³ + t¹⁵

2t⁷

2t¹¹

t⁷ + t¹⁹

2t¹¹

2t¹⁵

2t¹¹

t³ + t¹⁵

t⁷ + t¹⁹

2t⁹

t + t¹³

t⁵ + t¹⁷

2t¹³

t⁵ + t¹⁷

t⁹ + t²¹

t⁵ + t¹⁷

2t⁹

2t¹³

t¹⁰

t²

2t⁶

t⁴

t⁸

2t⁴

t⁸

t⁶

t⁸

2t⁶

2t⁴

t⁵

2t³

ϕ_2,11'''

2t¹³

t⁵ + t¹⁷

2t⁹

t⁵ + t¹⁷

2t⁹

t + t¹³

t⁹ + t²¹

2t¹³

t⁵ + t¹⁷

t⁷ + t¹⁹

2t¹¹

t³ + t¹⁵

2t¹¹

t³ + t¹⁵

2t⁷

2t¹⁵

t⁷ + t¹⁹

2t¹¹

t⁸

t¹⁰

t⁸

2t⁴

t²

2t⁶

t²

2t⁶

t⁴

t⁶

2t⁴

t²

t⁵

2t³

ϕ_2,9'''

t³ + t¹⁵

t⁷ + t¹⁹

2t¹¹

2t⁷

2t¹¹

t³ + t¹⁵

2t¹¹

2t¹⁵

t⁷ + t¹⁹

2t⁹

2t¹³

t⁵ + t¹⁷

t + t¹³

t⁵ + t¹⁷

2t⁹

t⁵ + t¹⁷

t⁹ + t²¹

2t¹³

t²

t¹⁰

t²

2t⁶

2t⁴

t⁸

t⁴

t⁸

2t⁶

t⁸

t⁶

2t⁴

t⁵

2t³

ϕ_2,7'''

t⁵ + t¹⁷

2t⁹

2t¹³

2t⁹

t + t¹³

t⁵ + t¹⁷

2t¹³

t⁵ + t¹⁷

t⁹ + t²¹

2t¹¹

t³ + t¹⁵

t⁷ + t¹⁹

t³ + t¹⁵

2t⁷

2t¹¹

t⁷ + t¹⁹

2t¹¹

2t¹⁵

t²

2t⁴

t⁴

t²

2t⁴

t²

t⁸

2t⁶

t¹⁰

t⁸

t⁶

2t³

t⁵

ϕ_2,15

t⁹ + t²¹

2t¹³

t⁵ + t¹⁷

2t¹³

t⁵ + t¹⁷

2t⁹

t⁵ + t¹⁷

2t⁹

t + t¹³

2t¹⁵

t⁷ + t¹⁹

2t¹¹

t⁷ + t¹⁹

2t¹¹

t³ + t¹⁵

2t¹¹

t³ + t¹⁵

2t⁷

t⁶

2t⁴

t⁸

2t⁴

t⁸

2t⁶

t⁸

2t⁶

t⁴

t²

t¹⁰

t⁵

2t³

ϕ_2,13'

2t¹¹

2t¹⁵

t⁷ + t¹⁹

t³ + t¹⁵

t⁷ + t¹⁹

2t¹¹

2t⁷

2t¹¹

t³ + t¹⁵

t⁵ + t¹⁷

t⁹ + t²¹

2t¹³

2t⁹

2t¹³

t⁵ + t¹⁷

t + t¹³

t⁵ + t¹⁷

2t⁹

t⁸

t⁶

2t⁶

t⁸

t¹⁰

t⁸

2t⁶

t²

2t⁴

t²

t⁴

t²

2t³

t⁵

ϕ_2,5'

t⁷ + t¹⁹

2t¹¹

2t¹⁵

2t¹¹

t³ + t¹⁵

t⁷ + t¹⁹

t³ + t¹⁵

2t⁷

2t¹¹

2t¹³

t⁵ + t¹⁷

t⁹ + t²¹

t⁵ + t¹⁷

2t⁹

2t¹³

2t⁹

t + t¹³

t⁵ + t¹⁷

2t⁴

t²

t⁶

t²

2t⁶

2t⁴

2t⁶

t⁴

t²

t⁸

t¹⁰

t⁸

t⁵

2t³

ϕ_2,13''

2t¹¹

t³ + t¹⁵

2t⁷

2t¹⁵

t⁷ + t¹⁹

2t¹¹

t⁷ + t¹⁹

2t¹¹

t³ + t¹⁵

t⁵ + t¹⁷

2t⁹

t + t¹³

t⁹ + t²¹

2t¹³

t⁵ + t¹⁷

2t¹³

t⁵ + t¹⁷

2t⁹

t⁸

2t⁶

t¹⁰

t⁶

t⁸

2t⁶

t²

t⁴

2t⁴

t²

2t⁴

t²

2t³

t⁵

ϕ_2,5''

2t⁷

2t¹¹

t³ + t¹⁵

2t¹¹

2t¹⁵

t⁷ + t¹⁹

t³ + t¹⁵

t⁷ + t¹⁹

2t¹¹

t + t¹³

t⁵ + t¹⁷

2t⁹

t⁵ + t¹⁷

t⁹ + t²¹

2t¹³

2t⁹

2t¹³

t⁵ + t¹⁷

t⁴

t²

2t⁶

t²

t⁶

2t⁴

2t⁶

2t⁴

t²

t¹⁰

t⁸

t⁵

2t³

ϕ_2,3'

2t⁹

t + t¹³

t⁵ + t¹⁷

2t¹³

t⁵ + t¹⁷

t⁹ + t²¹

t⁵ + t¹⁷

2t⁹

2t¹³

t³ + t¹⁵

2t⁷

2t¹¹

t⁷ + t¹⁹

2t¹¹

2t¹⁵

2t¹¹

t³ + t¹⁵

t⁷ + t¹⁹

2t⁶

t⁴

t⁸

2t⁴

t⁸

t⁶

t⁸

2t⁶

2t⁴

t¹⁰

t²

t⁵

2t³

ϕ_2,5'''

t⁷ + t¹⁹

2t¹¹

t³ + t¹⁵

2t¹¹

t³ + t¹⁵

2t⁷

2t¹⁵

t⁷ + t¹⁹

2t¹¹

2t¹³

t⁵ + t¹⁷

2t⁹

t⁵ + t¹⁷

2t⁹

t + t¹³

t⁹ + t²¹

2t¹³

t⁵ + t¹⁷

2t⁴

t²

2t⁶

t²

2t⁶

t⁴

t⁶

2t⁴

t²

t⁸

t¹⁰

t⁸

t⁵

2t³

ϕ_2,3''

2t⁹

2t¹³

t⁵ + t¹⁷

t + t¹³

t⁵ + t¹⁷

2t⁹

t⁵ + t¹⁷

t⁹ + t²¹

2t¹³

t³ + t¹⁵

t⁷ + t¹⁹

2t¹¹

2t⁷

2t¹¹

t³ + t¹⁵

2t¹¹

2t¹⁵

t⁷ + t¹⁹

2t⁶

2t⁴

t⁸

t⁴

t⁸

2t⁶

t⁸

t⁶

2t⁴

t²

t¹⁰

t²

t⁵

2t³

ϕ_2,1

2t¹¹

t³ + t¹⁵

t⁷ + t¹⁹

t³ + t¹⁵

2t⁷

2t¹¹

t⁷ + t¹⁹

2t¹¹

2t¹⁵

t⁵ + t¹⁷

2t⁹

2t¹³

2t⁹

t + t¹³

t⁵ + t¹⁷

2t¹³

t⁵ + t¹⁷

t⁹ + t²¹

t⁸

2t⁶

t¹⁰

t⁸

t⁶

t²

2t⁴

t⁴

t²

2t⁴

t²

2t³

t⁵

ϕ_3,10

t² + 2t¹⁴

2t⁶ + t¹⁸

3t¹⁰

2t⁶ + t¹⁸

3t¹⁰

t² + 2t¹⁴

3t¹⁰

t² + 2t¹⁴

2t⁶ + t¹⁸

2t⁸ + t²⁰

3t¹²

t⁴ + 2t¹⁶

3t¹²

t⁴ + 2t¹⁶

2t⁸ + t²⁰

t⁴ + 2t¹⁶

2t⁸ + t²⁰

3t¹²

t⁹

3t⁵

2t³

2t⁷

2t³

2t⁷

3t⁵

2t⁷

3t⁵

2t³

t⁶

2t⁴

2t²

ϕ_3,4

2t⁸ + t²⁰

3t¹²

t⁴ + 2t¹⁶

3t¹²

t⁴ + 2t¹⁶

2t⁸ + t²⁰

t⁴ + 2t¹⁶

2t⁸ + t²⁰

3t¹²

t² + 2t¹⁴

2t⁶ + t¹⁸

3t¹⁰

2t⁶ + t¹⁸

3t¹⁰

t² + 2t¹⁴

3t¹⁰

t² + 2t¹⁴

2t⁶ + t¹⁸

3t⁵

2t³

2t⁷

2t³

2t⁷

3t⁵

2t⁷

3t⁵

2t³

t⁹

t⁶

2t⁴

2t²

ϕ_3,2

3t¹⁰

t² + 2t¹⁴

2t⁶ + t¹⁸

t² + 2t¹⁴

2t⁶ + t¹⁸

3t¹⁰

2t⁶ + t¹⁸

3t¹⁰

t² + 2t¹⁴

t⁴ + 2t¹⁶

2t⁸ + t²⁰

3t¹²

2t⁸ + t²⁰

3t¹²

t⁴ + 2t¹⁶

3t¹²

t⁴ + 2t¹⁶

2t⁸ + t²⁰

2t⁷

3t⁵

t⁹

3t⁵

t⁹

2t⁷

t⁹

2t⁷

3t⁵

2t³

2t²

t⁶

2t⁴

ϕ_3,8

t⁴ + 2t¹⁶

2t⁸ + t²⁰

3t¹²

2t⁸ + t²⁰

3t¹²

t⁴ + 2t¹⁶

3t¹²

t⁴ + 2t¹⁶

2t⁸ + t²⁰

3t¹⁰

t² + 2t¹⁴

2t⁶ + t¹⁸

t² + 2t¹⁴

2t⁶ + t¹⁸

3t¹⁰

2t⁶ + t¹⁸

3t¹⁰

t² + 2t¹⁴

2t³

2t⁷

3t⁵

t⁹

3t⁵

t⁹

2t⁷

t⁹

2t⁷

3t⁵

2t²

t⁶

2t⁴

ϕ_3,6

2t⁶ + t¹⁸

3t¹⁰

t² + 2t¹⁴

3t¹⁰

t² + 2t¹⁴

2t⁶ + t¹⁸

t² + 2t¹⁴

2t⁶ + t¹⁸

3t¹⁰

3t¹²

t⁴ + 2t¹⁶

2t⁸ + t²⁰

t⁴ + 2t¹⁶

2t⁸ + t²⁰

3t¹²

2t⁸ + t²⁰

3t¹²

t⁴ + 2t¹⁶

2t³

3t⁵

2t³

3t⁵

2t³

t⁹

2t⁷

t⁹

2t⁷

2t⁴

2t²

t⁶

ϕ_3,12

3t¹²

t⁴ + 2t¹⁶

2t⁸ + t²⁰

t⁴ + 2t¹⁶

2t⁸ + t²⁰

3t¹²

2t⁸ + t²⁰

3t¹²

t⁴ + 2t¹⁶

2t⁶ + t¹⁸

3t¹⁰

t² + 2t¹⁴

3t¹⁰

t² + 2t¹⁴

2t⁶ + t¹⁸

t² + 2t¹⁴

2t⁶ + t¹⁸

3t¹⁰

t⁹

2t⁷

t⁹

2t⁷

2t³

3t⁵

2t³

3t⁵

2t³

2t⁴

2t²

t⁶

Exceptional hyperplanes

Unknown

The representation theory of the restricted rational Cherednik algebra for G7

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 G₇