The representation theory of the restricted rational Cherednik algebra for G22

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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Quick navigation: Exceptional hyperplanes

For generic parameters

Non-singleton Calogero–Moser families

{ϕ3,2,  ϕ3,6},   {ϕ3,12,  ϕ3,16},   {ϕ4,3,  ϕ4,6,  ϕ4,9,  ϕ2,11,  ϕ4,8,  ϕ2,13,  ϕ2,1,  ϕ2,7,  ϕ6,7,  ϕ6,5}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,024011 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 9t8 + 10t9 + 11t10 + 12t11 + 12t12 + 12t13 + 12t14 + 12t15 + 12t16 + 12t17 + 12t18 + 12t19 + 11t20 + 10t21 + 9t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ1,3024011 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 9t8 + 10t9 + 11t10 + 12t11 + 12t12 + 12t13 + 12t14 + 12t15 + 12t16 + 12t17 + 12t18 + 12t19 + 11t20 + 10t21 + 9t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ2,11822 + 4t + 2t2
ϕ2,13242
ϕ2,1822 + 4t + 2t2
ϕ2,7242
ϕ3,214433 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 12t8 + 12t9 + 12t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,64863 + 6t + 9t2 + 12t3 + 9t4 + 6t5 + 3t6
ϕ3,1214433 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 12t8 + 12t9 + 12t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,164863 + 6t + 9t2 + 12t3 + 9t4 + 6t5 + 3t6
ϕ4,31684 + 8t + 4t2
ϕ4,64164
ϕ4,91684 + 8t + 4t2
ϕ4,84164
ϕ5,424055 + 10t + 15t2 + 20t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 15t12 + 10t13 + 5t14
ϕ5,1024055 + 10t + 15t2 + 20t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 15t12 + 10t13 + 5t14
ϕ6,720186 + 8t + 6t2
ϕ6,520186 + 8t + 6t2

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,30) L(ϕ2,11) L(ϕ2,13) L(ϕ2,1) L(ϕ2,7) L(ϕ3,2) L(ϕ3,6) L(ϕ3,12) L(ϕ3,16) L(ϕ4,3) L(ϕ4,6) L(ϕ4,9) L(ϕ4,8) L(ϕ5,4) L(ϕ5,10) L(ϕ6,7) L(ϕ6,5)
ϕ1,0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 0
ϕ1,30 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0
ϕ2,11 2 2 1 0 1 0 2 0 2 0 0 0 0 0 2 2 0 0
ϕ2,13 2 2 0 1 0 0 2 0 0 1 0 0 0 0 2 2 0 0
ϕ2,1 2 2 1 0 1 0 2 0 2 0 0 0 0 0 2 2 0 0
ϕ2,7 2 2 0 0 0 1 0 1 2 0 0 0 0 0 2 2 0 0
ϕ3,2 3 3 1 0 0 0 3 0 3 0 1 0 0 0 3 3 0 0
ϕ3,6 3 3 0 0 0 0 1 1 1 1 0 0 0 0 3 3 1 0
ϕ3,12 3 3 0 0 1 0 3 0 3 0 0 0 1 0 3 3 0 0
ϕ3,16 3 3 0 0 0 0 1 1 1 1 0 0 0 0 3 3 0 1
ϕ4,3 4 4 0 0 0 0 2 1 4 0 1 0 1 0 4 4 0 0
ϕ4,6 4 4 0 0 0 0 2 1 2 1 0 1 0 0 4 4 0 0
ϕ4,9 4 4 0 0 0 0 4 0 2 1 1 0 1 0 4 4 0 0
ϕ4,8 4 4 0 0 0 0 2 1 2 1 0 0 0 1 4 4 0 0
ϕ5,4 5 5 0 0 0 0 3 1 3 1 0 0 1 0 5 5 0 1
ϕ5,10 5 5 0 0 0 0 3 1 3 1 1 0 0 0 5 5 1 0
ϕ6,7 6 6 0 0 0 0 4 1 2 2 0 0 0 0 6 6 1 1
ϕ6,5 6 6 0 0 0 0 2 2 4 1 0 0 0 0 6 6 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,30) L(ϕ2,11) L(ϕ2,13) L(ϕ2,1) L(ϕ2,7) L(ϕ3,2) L(ϕ3,6) L(ϕ3,12) L(ϕ3,16) L(ϕ4,3) L(ϕ4,6) L(ϕ4,9) L(ϕ4,8) L(ϕ5,4) L(ϕ5,10) L(ϕ6,7) L(ϕ6,5)
ϕ1,0 1 t30 0 0 t 0 t2 0 t12 0 0 0 0 0 t4 t10 0 0
ϕ1,30 t30 1 t 0 0 0 t12 0 t2 0 0 0 0 0 t10 t4 0 0
ϕ2,11 t + t29 t11 + t19 1 0 t2 0 t3 + t11 0 t + t13 0 0 0 0 0 t5 + t9 t3 + t11 0 0
ϕ2,13 t7 + t23 t13 + t17 0 1 0 0 t5 + t9 0 0 t3 0 0 0 0 t3 + t11 t5 + t9 0 0
ϕ2,1 t11 + t19 t + t29 t2 0 1 0 t + t13 0 t3 + t11 0 0 0 0 0 t3 + t11 t5 + t9 0 0
ϕ2,7 t13 + t17 t7 + t23 0 0 0 1 0 t3 t5 + t9 0 0 0 0 0 t5 + t9 t3 + t11 0 0
ϕ3,2 t2 + t10 + t18 t12 + t20 + t28 t 0 0 0 1 + t4 + t12 0 t2 + t10 + t14 0 t 0 0 0 t2 + t6 + t10 t4 + t8 + t12 0 0
ϕ3,6 t6 + t10 + t14 t16 + t20 + t24 0 0 0 0 t8 1 t6 t6 0 0 0 0 t2 + t6 + t10 t4 + t8 + t12 t 0
ϕ3,12 t12 + t20 + t28 t2 + t10 + t18 0 0 t 0 t2 + t10 + t14 0 1 + t4 + t12 0 0 0 t 0 t4 + t8 + t12 t2 + t6 + t10 0 0
ϕ3,16 t16 + t20 + t24 t6 + t10 + t14 0 0 0 0 t6 t6 t8 1 0 0 0 0 t4 + t8 + t12 t2 + t6 + t10 0 t
ϕ4,3 t9 + t13 + t17 + t21 t3 + t11 + t19 + t27 0 0 0 0 t3 + t11 t3 t + t5 + t9 + t13 0 1 0 t2 0 t + t5 + t9 + t13 t3 + 2t7 + t11 0 0
ϕ4,6 t6 + t14 + t18 + t22 t8 + t12 + t16 + t24 0 0 0 0 t4 + t8 t4 t6 + t10 t2 0 1 0 0 t2 + t6 + 2t10 2t4 + t8 + t12 0 0
ϕ4,9 t3 + t11 + t19 + t27 t9 + t13 + t17 + t21 0 0 0 0 t + t5 + t9 + t13 0 t3 + t11 t3 t2 0 1 0 t3 + 2t7 + t11 t + t5 + t9 + t13 0 0
ϕ4,8 t8 + t12 + t16 + t24 t6 + t14 + t18 + t22 0 0 0 0 t6 + t10 t2 t4 + t8 t4 0 0 0 1 2t4 + t8 + t12 t2 + t6 + 2t10 0 0
ϕ5,4 t4 + t8 + t12 + t16 + t20 t10 + t14 + t18 + t22 + t26 0 0 0 0 t2 + t6 + t10 t2 t4 + t8 + t12 t4 0 0 t 0 1 + t4 + 2t8 + t12 t2 + 2t6 + t10 + t14 0 t
ϕ5,10 t10 + t14 + t18 + t22 + t26 t4 + t8 + t12 + t16 + t20 0 0 0 0 t4 + t8 + t12 t4 t2 + t6 + t10 t2 t 0 0 0 t2 + 2t6 + t10 + t14 1 + t4 + 2t8 + t12 t 0
ϕ6,7 t5 + t9 + t13 + t17 + t21 + t25 t7 + t11 + 2t15 + t19 + t23 0 0 0 0 t3 + 2t7 + t11 t3 t5 + t9 t + t5 0 0 0 0 t + 2t5 + 2t9 + t13 2t3 + 2t7 + 2t11 1 t2
ϕ6,5 t7 + t11 + 2t15 + t19 + t23 t5 + t9 + t13 + t17 + t21 + t25 0 0 0 0 t5 + t9 t + t5 t3 + 2t7 + t11 t3 0 0 0 0 2t3 + 2t7 + 2t11 t + 2t5 + 2t9 + t13 t2 1

Exceptional hyperplanes

There are none.