The representation theory of the restricted rational Cherednik algebra for G24

Computed by Ulrich Thiel using CHAMP (see LMS J. Comput. Math., 2015). Last update on Fri Mar 27 12:48:22 CET 2015.

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Quick navigation: Exceptional hyperplanes

For generic parameters

Non-singleton Calogero–Moser families

{ϕ3,8,  ϕ3,10,  ϕ6,9},   {ϕ3,1,  ϕ3,3,  ϕ6,2},   {ϕ8,4,  ϕ8,5}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,033611 + 3t + 6t2 + 10t3 + 14t4 + 18t5 + 21t6 + 23t7 + 24t8 + 24t9 + 24t10 + 24t11 + 24t12 + 24t13 + 23t14 + 21t15 + 18t16 + 14t17 + 10t18 + 6t19 + 3t20 + t21
ϕ1,2133611 + 3t + 6t2 + 10t3 + 14t4 + 18t5 + 21t6 + 23t7 + 24t8 + 24t9 + 24t10 + 24t11 + 24t12 + 24t13 + 23t14 + 21t15 + 18t16 + 14t17 + 10t18 + 6t19 + 3t20 + t21
ϕ3,815633 + 9t + 18t2 + 24t3 + 24t4 + 24t5 + 24t6 + 18t7 + 9t8 + 3t9
ϕ3,115633 + 9t + 18t2 + 24t3 + 24t4 + 24t5 + 24t6 + 18t7 + 9t8 + 3t9
ϕ3,10663 + 3t
ϕ3,3663 + 3t
ϕ6,242246 + 15t + 15t2 + 6t3
ϕ6,942246 + 15t + 15t2 + 6t3
ϕ7,633677 + 21t + 35t2 + 49t3 + 56t4 + 56t5 + 49t6 + 35t7 + 21t8 + 7t9
ϕ7,333677 + 21t + 35t2 + 49t3 + 56t4 + 56t5 + 49t6 + 35t7 + 21t8 + 7t9
ϕ8,416888 + 16t + 24t2 + 24t3 + 24t4 + 24t5 + 24t6 + 16t7 + 8t8
ϕ8,516888 + 16t + 24t2 + 24t3 + 24t4 + 24t5 + 24t6 + 16t7 + 8t8

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,21) L(ϕ3,8) L(ϕ3,1) L(ϕ3,10) L(ϕ3,3) L(ϕ6,2) L(ϕ6,9) L(ϕ7,6) L(ϕ7,3) L(ϕ8,4) L(ϕ8,5)
ϕ1,0 1 1 1 1 0 0 0 0 1 1 1 0
ϕ1,21 1 1 1 1 0 0 0 0 1 1 0 1
ϕ3,8 3 3 3 1 0 1 0 0 3 3 1 2
ϕ3,1 3 3 1 3 1 0 0 0 3 3 2 1
ϕ3,10 3 3 1 3 1 0 0 0 3 3 1 2
ϕ3,3 3 3 3 1 0 1 0 0 3 3 2 1
ϕ6,2 6 6 2 2 0 0 1 1 6 6 2 4
ϕ6,9 6 6 2 2 0 0 1 1 6 6 4 2
ϕ7,6 7 7 3 3 0 0 1 1 7 7 3 4
ϕ7,3 7 7 3 3 0 0 1 1 7 7 4 3
ϕ8,4 8 8 4 4 0 0 1 1 8 8 6 2
ϕ8,5 8 8 4 4 0 0 1 1 8 8 2 6

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,21) L(ϕ3,8) L(ϕ3,1) L(ϕ3,10) L(ϕ3,3) L(ϕ6,2) L(ϕ6,9) L(ϕ7,6) L(ϕ7,3) L(ϕ8,4) L(ϕ8,5)
ϕ1,0 1 t21 t8 t 0 0 0 0 t6 t3 t4 0
ϕ1,21 t21 1 t t8 0 0 0 0 t3 t6 0 t4
ϕ3,8 t10 + t12 + t20 t3 + t5 + t13 1 + t4 + t6 t7 0 t 0 0 t2 + t4 + t6 t3 + t5 + t7 t2 t3 + t7
ϕ3,1 t3 + t5 + t13 t10 + t12 + t20 t7 1 + t4 + t6 t 0 0 0 t3 + t5 + t7 t2 + t4 + t6 t3 + t7 t2
ϕ3,10 t8 + t16 + t18 t + t9 + t11 t2 t3 + t5 + t9 1 0 0 0 t2 + t4 + t6 t3 + t5 + t7 t6 t + t5
ϕ3,3 t + t9 + t11 t8 + t16 + t18 t3 + t5 + t9 t2 0 1 0 0 t3 + t5 + t7 t2 + t4 + t6 t + t5 t6
ϕ6,2 t2 + t4 + t6 + t8 + t10 + t12 t9 + t11 + t13 + t15 + t17 + t19 t4 + t6 t3 + t5 0 0 1 t3 t2 + 2t4 + 2t6 + t8 t + 2t3 + 2t5 + t7 t2 + t6 t + t3 + t5 + t7
ϕ6,9 t9 + t11 + t13 + t15 + t17 + t19 t2 + t4 + t6 + t8 + t10 + t12 t3 + t5 t4 + t6 0 0 t3 1 t + 2t3 + 2t5 + t7 t2 + 2t4 + 2t6 + t8 t + t3 + t5 + t7 t2 + t6
ϕ7,6 t6 + t8 + t10 + t12 + t14 + t16 + t18 t3 + t5 + t7 + t9 + t11 + t13 + t15 t2 + t4 + t6 t3 + t5 + t7 0 0 t2 t 1 + t2 + 2t4 + 2t6 + t8 t + 2t3 + 2t5 + t7 + t9 t2 + t4 + t6 t + t3 + t5 + t7
ϕ7,3 t3 + t5 + t7 + t9 + t11 + t13 + t15 t6 + t8 + t10 + t12 + t14 + t16 + t18 t3 + t5 + t7 t2 + t4 + t6 0 0 t t2 t + 2t3 + 2t5 + t7 + t9 1 + t2 + 2t4 + 2t6 + t8 t + t3 + t5 + t7 t2 + t4 + t6
ϕ8,4 t4 + t6 + t8 + t10 + t12 + 2t14 + t16 t5 + 2t7 + t9 + t11 + t13 + t15 + t17 t2 + t4 + t6 + t8 t + t3 + t5 + t7 0 0 t2 t 2t2 + 3t4 + 2t6 + t8 t + 2t3 + 3t5 + 2t7 1 + t2 + 2t4 + t6 + t8 t3 + t5
ϕ8,5 t5 + 2t7 + t9 + t11 + t13 + t15 + t17 t4 + t6 + t8 + t10 + t12 + 2t14 + t16 t + t3 + t5 + t7 t2 + t4 + t6 + t8 0 0 t t2 t + 2t3 + 3t5 + 2t7 2t2 + 3t4 + 2t6 + t8 t3 + t5 1 + t2 + 2t4 + t6 + t8

Exceptional hyperplanes

There are none.