The representation theory of the restricted rational Cherednik algebra for G23

Computed by Ulrich Thiel using CHAMP (see LMS J. Comput. Math., 2015). Last update on Fri Mar 27 12:48:21 CET 2015.

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For generic parameters

Non-singleton Calogero–Moser families

{ϕ3,1,  ϕ3,3},   {ϕ4,3,  ϕ4,4},   {ϕ3,6,  ϕ3,8}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,1512011 + 3t + 5t2 + 7t3 + 9t4 + 11t5 + 12t6 + 12t7 + 12t8 + 12t9 + 11t10 + 9t11 + 7t12 + 5t13 + 3t14 + t15
ϕ1,012011 + 3t + 5t2 + 7t3 + 9t4 + 11t5 + 12t6 + 12t7 + 12t8 + 12t9 + 11t10 + 9t11 + 7t12 + 5t13 + 3t14 + t15
ϕ5,512055 + 15t + 20t2 + 20t3 + 20t4 + 20t5 + 15t6 + 5t7
ϕ5,212055 + 15t + 20t2 + 20t3 + 20t4 + 20t5 + 15t6 + 5t7
ϕ3,67233 + 9t + 12t2 + 12t3 + 12t4 + 12t5 + 9t6 + 3t7
ϕ3,82463 + 9t + 9t2 + 3t3
ϕ3,17233 + 9t + 12t2 + 12t3 + 12t4 + 12t5 + 9t6 + 3t7
ϕ3,32463 + 9t + 9t2 + 3t3
ϕ4,36044 + 8t + 12t2 + 12t3 + 12t4 + 8t5 + 4t6
ϕ4,46044 + 8t + 12t2 + 12t3 + 12t4 + 8t5 + 4t6

Characters of the simple modules

ϕ L(ϕ1,15) L(ϕ1,0) L(ϕ5,5) L(ϕ5,2) L(ϕ3,6) L(ϕ3,8) L(ϕ3,1) L(ϕ3,3) L(ϕ4,3) L(ϕ4,4)
ϕ1,15 1 1 1 1 1 0 1 0 0 1
ϕ1,0 1 1 1 1 1 0 1 0 1 0
ϕ5,5 5 5 5 5 3 1 3 1 2 3
ϕ5,2 5 5 5 5 3 1 3 1 3 2
ϕ3,6 3 3 3 3 3 0 3 0 1 2
ϕ3,8 3 3 3 3 1 1 1 1 3 0
ϕ3,1 3 3 3 3 3 0 3 0 2 1
ϕ3,3 3 3 3 3 1 1 1 1 0 3
ϕ4,3 4 4 4 4 2 1 2 1 4 0
ϕ4,4 4 4 4 4 2 1 2 1 0 4

Graded characters of the simple modules

ϕ L(ϕ1,15) L(ϕ1,0) L(ϕ5,5) L(ϕ5,2) L(ϕ3,6) L(ϕ3,8) L(ϕ3,1) L(ϕ3,3) L(ϕ4,3) L(ϕ4,4)
ϕ1,15 1 t15 t2 t5 t 0 t6 0 0 t3
ϕ1,0 t15 1 t5 t2 t6 0 t 0 t3 0
ϕ5,5 t2 + t4 + t6 + t8 + t10 t5 + t7 + t9 + t11 + t13 1 + t2 + 2t4 + t6 t + 2t3 + t5 + t7 t + t3 + t5 t t2 + t4 + t6 t2 t2 + t4 t + t3 + t5
ϕ5,2 t5 + t7 + t9 + t11 + t13 t2 + t4 + t6 + t8 + t10 t + 2t3 + t5 + t7 1 + t2 + 2t4 + t6 t2 + t4 + t6 t2 t + t3 + t5 t t + t3 + t5 t2 + t4
ϕ3,6 t + t5 + t9 t6 + t10 + t14 t + t3 + t5 t2 + t4 + t6 1 + t2 + t6 0 t + t5 + t7 0 t3 t2 + t4
ϕ3,8 t3 + t5 + t7 t8 + t10 + t12 t + t3 + t5 t2 + t4 + t6 t4 1 t3 t3 t + t3 + t5 0
ϕ3,1 t6 + t10 + t14 t + t5 + t9 t2 + t4 + t6 t + t3 + t5 t + t5 + t7 0 1 + t2 + t6 0 t2 + t4 t3
ϕ3,3 t8 + t10 + t12 t3 + t5 + t7 t2 + t4 + t6 t + t3 + t5 t3 t3 t4 1 0 t + t3 + t5
ϕ4,3 t4 + t6 + t8 + t12 t3 + t7 + t9 + t11 2t2 + t4 + t6 t + t3 + 2t5 t3 + t5 t t2 + t4 t2 1 + t2 + t4 + t6 0
ϕ4,4 t3 + t7 + t9 + t11 t4 + t6 + t8 + t12 t + t3 + 2t5 2t2 + t4 + t6 t2 + t4 t2 t3 + t5 t 0 1 + t2 + t4 + t6

Exceptional hyperplanes

There are none.