The representation theory of the restricted rational Cherednik algebra for G9

Computed by Ulrich Thiel using CHAMP (see LMS J. Comput. Math., 2015). Last update on Fri Mar 27 12:48:15 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

{ϕ2,13,  ϕ2,17},   {ϕ2,7'',  ϕ2,11''},   {ϕ2,8,  ϕ2,4},   {ϕ2,1,  ϕ2,5},   {ϕ2,7',  ϕ2,11'},   {ϕ4,9,  ϕ4,7,  ϕ4,3,  ϕ4,5},   {ϕ2,10,  ϕ2,14}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,019211 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 8t12 + 8t13 + 8t14 + 8t15 + 8t16 + 8t17 + 8t18 + 8t19 + 8t20 + 8t21 + 8t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ1,619211 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 8t12 + 8t13 + 8t14 + 8t15 + 8t16 + 8t17 + 8t18 + 8t19 + 8t20 + 8t21 + 8t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ1,12''19211 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 8t12 + 8t13 + 8t14 + 8t15 + 8t16 + 8t17 + 8t18 + 8t19 + 8t20 + 8t21 + 8t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ1,18''19211 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 8t12 + 8t13 + 8t14 + 8t15 + 8t16 + 8t17 + 8t18 + 8t19 + 8t20 + 8t21 + 8t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ1,12'19211 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 8t12 + 8t13 + 8t14 + 8t15 + 8t16 + 8t17 + 8t18 + 8t19 + 8t20 + 8t21 + 8t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ1,18'19211 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 8t12 + 8t13 + 8t14 + 8t15 + 8t16 + 8t17 + 8t18 + 8t19 + 8t20 + 8t21 + 8t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ1,2419211 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 8t12 + 8t13 + 8t14 + 8t15 + 8t16 + 8t17 + 8t18 + 8t19 + 8t20 + 8t21 + 8t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ1,3019211 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 8t12 + 8t13 + 8t14 + 8t15 + 8t16 + 8t17 + 8t18 + 8t19 + 8t20 + 8t21 + 8t22 + 8t23 + 7t24 + 6t25 + 5t26 + 4t27 + 3t28 + 2t29 + t30
ϕ2,59622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,49622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,7''9622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,7'9622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,109622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,139622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,19622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,149622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,179622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,11''9622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,11'9622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,89622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ3,8''19233 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 21t8 + 18t9 + 15t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,6''19233 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 21t8 + 18t9 + 15t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,419233 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 21t8 + 18t9 + 15t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,219233 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 21t8 + 18t9 + 15t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,1219233 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 21t8 + 18t9 + 15t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,1019233 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 21t8 + 18t9 + 15t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,8'19233 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 21t8 + 18t9 + 15t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ3,6'19233 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 21t8 + 18t9 + 15t10 + 12t11 + 9t12 + 6t13 + 3t14
ϕ4,94844 + 8t + 8t2 + 8t3 + 8t4 + 8t5 + 4t6
ϕ4,74844 + 8t + 8t2 + 8t3 + 8t4 + 8t5 + 4t6
ϕ4,34844 + 8t + 8t2 + 8t3 + 8t4 + 8t5 + 4t6
ϕ4,54844 + 8t + 8t2 + 8t3 + 8t4 + 8t5 + 4t6

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12'') L(ϕ1,18'') L(ϕ1,12') L(ϕ1,18') L(ϕ1,24) L(ϕ1,30) L(ϕ2,5) L(ϕ2,4) L(ϕ2,7'') L(ϕ2,7') L(ϕ2,10) L(ϕ2,13) L(ϕ2,1) L(ϕ2,14) L(ϕ2,17) L(ϕ2,11'') L(ϕ2,11') L(ϕ2,8) L(ϕ3,8'') L(ϕ3,6'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,12) L(ϕ3,10) L(ϕ3,8') L(ϕ3,6') L(ϕ4,9) L(ϕ4,7) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0
ϕ1,6 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0
ϕ1,12'' 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0
ϕ1,18'' 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1
ϕ1,12' 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0
ϕ1,18' 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1
ϕ1,24 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0
ϕ1,30 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0
ϕ2,5 2 2 2 2 2 2 2 2 2 0 0 1 1 1 0 1 1 2 1 2 2 2 2 2 2 2 2 2 1 1 0 0
ϕ2,4 2 2 2 2 2 2 2 2 1 2 2 2 2 1 1 0 1 0 0 0 2 2 2 2 2 2 2 2 1 0 0 1
ϕ2,7'' 2 2 2 2 2 2 2 2 1 1 2 1 2 2 1 0 0 0 1 1 2 2 2 2 2 2 2 2 1 0 1 0
ϕ2,7' 2 2 2 2 2 2 2 2 2 1 1 2 2 1 0 0 1 1 0 1 2 2 2 2 2 2 2 2 1 0 1 0
ϕ2,10 2 2 2 2 2 2 2 2 2 0 1 1 2 2 0 0 0 1 1 2 2 2 2 2 2 2 2 2 0 1 1 0
ϕ2,13 2 2 2 2 2 2 2 2 1 0 1 0 1 2 1 1 0 1 2 2 2 2 2 2 2 2 2 2 1 1 0 0
ϕ2,1 2 2 2 2 2 2 2 2 0 2 2 1 1 1 2 1 1 0 1 0 2 2 2 2 2 2 2 2 0 0 1 1
ϕ2,14 2 2 2 2 2 2 2 2 0 2 1 1 0 0 2 2 2 1 1 0 2 2 2 2 2 2 2 2 0 1 1 0
ϕ2,17 2 2 2 2 2 2 2 2 1 2 1 2 1 0 1 1 2 1 0 0 2 2 2 2 2 2 2 2 0 0 1 1
ϕ2,11'' 2 2 2 2 2 2 2 2 1 1 0 1 0 0 1 2 2 2 1 1 2 2 2 2 2 2 2 2 0 1 0 1
ϕ2,11' 2 2 2 2 2 2 2 2 0 1 1 0 0 1 2 2 1 1 2 1 2 2 2 2 2 2 2 2 0 1 0 1
ϕ2,8 2 2 2 2 2 2 2 2 1 0 0 0 0 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 1 0 0 1
ϕ3,8'' 3 3 3 3 3 3 3 3 2 2 1 1 2 1 1 1 2 2 2 1 3 3 3 3 3 3 3 3 1 0 1 1
ϕ3,6'' 3 3 3 3 3 3 3 3 1 1 2 1 2 1 2 1 2 1 2 2 3 3 3 3 3 3 3 3 1 1 1 0
ϕ3,4 3 3 3 3 3 3 3 3 2 1 2 2 1 1 1 2 2 1 1 2 3 3 3 3 3 3 3 3 1 1 0 1
ϕ3,2 3 3 3 3 3 3 3 3 2 2 2 1 1 2 1 2 1 1 2 1 3 3 3 3 3 3 3 3 0 1 1 1
ϕ3,12 3 3 3 3 3 3 3 3 1 1 2 2 1 2 2 2 1 1 1 2 3 3 3 3 3 3 3 3 1 1 0 1
ϕ3,10 3 3 3 3 3 3 3 3 2 2 1 2 1 2 1 2 1 2 1 1 3 3 3 3 3 3 3 3 0 1 1 1
ϕ3,8' 3 3 3 3 3 3 3 3 1 2 1 1 2 2 2 1 1 2 2 1 3 3 3 3 3 3 3 3 1 0 1 1
ϕ3,6' 3 3 3 3 3 3 3 3 1 1 1 2 2 1 2 1 2 2 1 2 3 3 3 3 3 3 3 3 1 1 1 0
ϕ4,9 4 4 4 4 4 4 4 4 3 2 1 1 2 3 1 2 1 3 3 2 4 4 4 4 4 4 4 4 1 1 1 1
ϕ4,7 4 4 4 4 4 4 4 4 1 2 1 1 2 1 3 2 3 3 3 2 4 4 4 4 4 4 4 4 1 1 1 1
ϕ4,3 4 4 4 4 4 4 4 4 3 2 3 3 2 3 1 2 1 1 1 2 4 4 4 4 4 4 4 4 1 1 1 1
ϕ4,5 4 4 4 4 4 4 4 4 1 2 3 3 2 1 3 2 3 1 1 2 4 4 4 4 4 4 4 4 1 1 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12'') L(ϕ1,18'') L(ϕ1,12') L(ϕ1,18') L(ϕ1,24) L(ϕ1,30) L(ϕ2,5) L(ϕ2,4) L(ϕ2,7'') L(ϕ2,7') L(ϕ2,10) L(ϕ2,13) L(ϕ2,1) L(ϕ2,14) L(ϕ2,17) L(ϕ2,11'') L(ϕ2,11') L(ϕ2,8) L(ϕ3,8'') L(ϕ3,6'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,12) L(ϕ3,10) L(ϕ3,8') L(ϕ3,6') L(ϕ4,9) L(ϕ4,7) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 t6 t12 t18 t12 t18 t24 t30 0 t4 t7 t7 t10 t13 t 0 0 0 0 0 t8 t6 t4 t2 t12 t10 t8 t6 0 0 t3 0
ϕ1,6 t18 1 t6 t12 t30 t12 t18 t24 t7 0 0 t t4 t7 0 0 0 t13 0 t10 t2 t8 t6 t4 t6 t12 t10 t8 t3 0 0 0
ϕ1,12'' t12 t18 1 t6 t24 t30 t12 t18 0 0 0 0 0 t t13 t10 0 t7 t7 t4 t4 t2 t8 t6 t8 t6 t12 t10 0 t3 0 0
ϕ1,18'' t6 t12 t18 1 t18 t24 t30 t12 0 t10 0 t13 0 0 t7 t4 t7 t 0 0 t6 t4 t2 t8 t10 t8 t6 t12 0 0 0 t3
ϕ1,12' t12 t18 t24 t30 1 t6 t12 t18 t 0 0 0 0 0 0 t10 t13 t7 t7 t4 t12 t10 t8 t6 t8 t6 t4 t2 0 t3 0 0
ϕ1,18' t30 t12 t18 t24 t18 1 t6 t12 0 t10 t13 0 0 0 t7 t4 t7 0 t 0 t6 t12 t10 t8 t2 t8 t6 t4 0 0 0 t3
ϕ1,24 t24 t30 t12 t18 t12 t18 1 t6 t13 t4 t7 t7 t10 0 0 0 t 0 0 0 t8 t6 t12 t10 t4 t2 t8 t6 0 0 t3 0
ϕ1,30 t18 t24 t30 t12 t6 t12 t18 1 t7 0 t 0 t4 t7 0 0 0 0 t13 t10 t10 t8 t6 t12 t6 t4 t2 t8 t3 0 0 0
ϕ2,5 t11 + t19 t + t17 t7 + t23 t13 + t29 t7 + t23 t5 + t13 t11 + t19 t17 + t25 1 + t8 0 0 t2 t5 t8 0 t9 t12 t6 + t14 t6 t3 + t11 t3 + t11 2t9 2t7 2t5 2t7 t5 + t13 t3 + t11 t + t9 t4 t2 0 0
ϕ2,4 t4 + t20 t10 + t26 t8 + t16 t14 + t22 t8 + t16 t14 + t22 t4 + t20 t10 + t26 t9 1 + t8 t3 + t11 t3 + t11 t6 + t14 t9 t5 0 t5 0 0 0 t4 + t12 t2 + t10 2t8 2t6 2t8 2t6 t4 + t12 t2 + t10 t5 0 0 t
ϕ2,7'' t + t17 t7 + t23 t13 + t29 t11 + t19 t5 + t13 t11 + t19 t17 + t25 t7 + t23 t6 t5 1 + t8 t8 t3 + t11 t6 + t14 t2 0 0 0 t12 t9 2t9 2t7 2t5 t3 + t11 t5 + t13 t3 + t11 t + t9 2t7 t2 0 t4 0
ϕ2,7' t17 + t25 t7 + t23 t5 + t13 t11 + t19 t13 + t29 t11 + t19 t + t17 t7 + t23 t6 + t14 t5 t8 1 + t8 t3 + t11 t6 0 0 t2 t12 0 t9 t + t9 2t7 t5 + t13 t3 + t11 2t5 t3 + t11 2t9 2t7 t2 0 t4 0
ϕ2,10 t14 + t22 t4 + t20 t10 + t26 t8 + t16 t10 + t26 t8 + t16 t14 + t22 t4 + t20 t3 + t11 0 t5 t5 1 + t8 t3 + t11 0 0 0 t9 t9 t6 + t14 2t6 t4 + t12 t2 + t10 2t8 t2 + t10 2t8 2t6 t4 + t12 0 t5 t 0
ϕ2,13 t11 + t19 t17 + t25 t7 + t23 t5 + t13 t7 + t23 t13 + t29 t11 + t19 t + t17 t8 0 t2 0 t5 1 + t8 t12 t9 0 t6 t6 + t14 t3 + t11 t3 + t11 t + t9 2t7 t5 + t13 2t7 2t5 t3 + t11 2t9 t4 t2 0 0
ϕ2,1 t7 + t23 t5 + t13 t11 + t19 t17 + t25 t11 + t19 t + t17 t7 + t23 t13 + t29 0 t3 + t11 t6 + t14 t6 t9 t12 1 + t8 t5 t8 0 t2 0 2t7 t5 + t13 t3 + t11 t + t9 t3 + t11 2t9 2t7 2t5 0 0 t2 t4
ϕ2,14 t10 + t26 t8 + t16 t14 + t22 t4 + t20 t14 + t22 t4 + t20 t10 + t26 t8 + t16 0 t6 + t14 t9 t9 0 0 t3 + t11 1 + t8 t3 + t11 t5 t5 0 t2 + t10 2t8 2t6 t4 + t12 2t6 t4 + t12 t2 + t10 2t8 0 t t5 0
ϕ2,17 t7 + t23 t13 + t29 t11 + t19 t + t17 t11 + t19 t17 + t25 t7 + t23 t5 + t13 t12 t3 + t11 t6 t6 + t14 t9 0 t8 t5 1 + t8 t2 0 0 2t7 2t5 t3 + t11 2t9 t3 + t11 t + t9 2t7 t5 + t13 0 0 t2 t4
ϕ2,11'' t5 + t13 t11 + t19 t17 + t25 t7 + t23 t + t17 t7 + t23 t13 + t29 t11 + t19 t2 t9 0 t12 0 0 t6 t3 + t11 t6 + t14 1 + t8 t8 t5 t5 + t13 t3 + t11 t + t9 2t7 2t9 2t7 2t5 t3 + t11 0 t4 0 t2
ϕ2,11' t13 + t29 t11 + t19 t + t17 t7 + t23 t17 + t25 t7 + t23 t5 + t13 t11 + t19 0 t9 t12 0 0 t2 t6 + t14 t3 + t11 t6 t8 1 + t8 t5 2t5 t3 + t11 2t9 2t7 t + t9 2t7 t5 + t13 t3 + t11 0 t4 0 t2
ϕ2,8 t8 + t16 t14 + t22 t4 + t20 t10 + t26 t4 + t20 t10 + t26 t8 + t16 t14 + t22 t5 0 0 0 0 t5 t9 t6 + t14 t9 t3 + t11 t3 + t11 1 + t8 2t8 2t6 t4 + t12 t2 + t10 t4 + t12 t2 + t10 2t8 2t6 t 0 0 t5
ϕ3,8'' t8 + t16 + t24 t6 + t14 + t22 t4 + t12 + t20 t2 + t10 + t18 t12 + t20 + t28 t10 + t18 + t26 t8 + t16 + t24 t6 + t14 + t22 t5 + t13 t4 + t12 t7 t7 t2 + t10 t5 t9 t6 t + t9 t3 + t11 t3 + t11 t8 1 + 2t8 3t6 2t4 + t12 t2 + 2t10 2t4 + t12 t2 + 2t10 3t8 2t6 + t14 t 0 t3 t5
ϕ3,6'' t2 + t10 + t18 t8 + t16 + t24 t6 + t14 + t22 t4 + t12 + t20 t6 + t14 + t22 t12 + t20 + t28 t10 + t18 + t26 t8 + t16 + t24 t7 t6 t + t9 t9 t4 + t12 t7 t3 + t11 t8 t3 + t11 t5 t5 + t13 t2 + t10 t2 + 2t10 1 + 2t8 3t6 2t4 + t12 2t6 + t14 2t4 + t12 t2 + 2t10 3t8 t3 t t5 0
ϕ3,4 t4 + t12 + t20 t2 + t10 + t18 t8 + t16 + t24 t6 + t14 + t22 t8 + t16 + t24 t6 + t14 + t22 t12 + t20 + t28 t10 + t18 + t26 t + t9 t8 t3 + t11 t3 + t11 t6 t9 t5 t2 + t10 t5 + t13 t7 t7 t4 + t12 2t4 + t12 t2 + 2t10 1 + 2t8 3t6 3t8 2t6 + t14 2t4 + t12 t2 + 2t10 t5 t3 0 t
ϕ3,2 t6 + t14 + t22 t4 + t12 + t20 t2 + t10 + t18 t8 + t16 + t24 t10 + t18 + t26 t8 + t16 + t24 t6 + t14 + t22 t12 + t20 + t28 t3 + t11 t2 + t10 t5 + t13 t5 t8 t3 + t11 t7 t4 + t12 t7 t9 t + t9 t6 3t6 2t4 + t12 t2 + 2t10 1 + 2t8 t2 + 2t10 3t8 2t6 + t14 2t4 + t12 0 t5 t t3
ϕ3,12 t12 + t20 + t28 t10 + t18 + t26 t8 + t16 + t24 t6 + t14 + t22 t8 + t16 + t24 t6 + t14 + t22 t4 + t12 + t20 t2 + t10 + t18 t9 t8 t3 + t11 t3 + t11 t6 t + t9 t5 + t13 t2 + t10 t5 t7 t7 t4 + t12 2t4 + t12 t2 + 2t10 3t8 2t6 + t14 1 + 2t8 3t6 2t4 + t12 t2 + 2t10 t5 t3 0 t
ϕ3,10 t6 + t14 + t22 t12 + t20 + t28 t10 + t18 + t26 t8 + t16 + t24 t2 + t10 + t18 t8 + t16 + t24 t6 + t14 + t22 t4 + t12 + t20 t3 + t11 t2 + t10 t5 t5 + t13 t8 t3 + t11 t7 t4 + t12 t7 t + t9 t9 t6 2t6 + t14 2t4 + t12 t2 + 2t10 3t8 t2 + 2t10 1 + 2t8 3t6 2t4 + t12 0 t5 t t3
ϕ3,8' t8 + t16 + t24 t6 + t14 + t22 t12 + t20 + t28 t10 + t18 + t26 t4 + t12 + t20 t2 + t10 + t18 t8 + t16 + t24 t6 + t14 + t22 t5 t4 + t12 t7 t7 t2 + t10 t5 + t13 t + t9 t6 t9 t3 + t11 t3 + t11 t8 3t8 2t6 + t14 2t4 + t12 t2 + 2t10 2t4 + t12 t2 + 2t10 1 + 2t8 3t6 t 0 t3 t5
ϕ3,6' t10 + t18 + t26 t8 + t16 + t24 t6 + t14 + t22 t12 + t20 + t28 t6 + t14 + t22 t4 + t12 + t20 t2 + t10 + t18 t8 + t16 + t24 t7 t6 t9 t + t9 t4 + t12 t7 t3 + t11 t8 t3 + t11 t5 + t13 t5 t2 + t10 t2 + 2t10 3t8 2t6 + t14 2t4 + t12 3t6 2t4 + t12 t2 + 2t10 1 + 2t8 t3 t t5 0
ϕ4,9 t7 + 2t15 + t23 t5 + t13 + 2t21 t3 + t11 + t19 + t27 2t9 + t17 + t25 t3 + t11 + t19 + t27 2t9 + t17 + t25 t7 + 2t15 + t23 t5 + t13 + 2t21 2t4 + t12 t3 + t11 t6 t6 t + t9 2t4 + t12 t8 t5 + t13 t8 t2 + 2t10 t2 + 2t10 2t7 4t7 3t5 + t13 2t3 + 2t11 t + 3t9 2t3 + 2t11 t + 3t9 4t7 3t5 + t13 1 t6 t2 t4
ϕ4,7 2t9 + t17 + t25 t7 + 2t15 + t23 t5 + t13 + 2t21 t3 + t11 + t19 + t27 t5 + t13 + 2t21 t3 + t11 + t19 + t27 2t9 + t17 + t25 t7 + 2t15 + t23 t6 t5 + t13 t8 t8 t3 + t11 t6 t2 + 2t10 2t7 t2 + 2t10 2t4 + t12 2t4 + t12 t + t9 t + 3t9 4t7 3t5 + t13 2t3 + 2t11 3t5 + t13 2t3 + 2t11 t + 3t9 4t7 t2 1 t4 t6
ϕ4,3 t5 + t13 + 2t21 t3 + t11 + t19 + t27 2t9 + t17 + t25 t7 + 2t15 + t23 2t9 + t17 + t25 t7 + 2t15 + t23 t5 + t13 + 2t21 t3 + t11 + t19 + t27 t2 + 2t10 t + t9 2t4 + t12 2t4 + t12 2t7 t2 + 2t10 t6 t3 + t11 t6 t8 t8 t5 + t13 3t5 + t13 2t3 + 2t11 t + 3t9 4t7 t + 3t9 4t7 3t5 + t13 2t3 + 2t11 t6 t4 1 t2
ϕ4,5 t3 + t11 + t19 + t27 2t9 + t17 + t25 t7 + 2t15 + t23 t5 + t13 + 2t21 t7 + 2t15 + t23 t5 + t13 + 2t21 t3 + t11 + t19 + t27 2t9 + t17 + t25 t8 2t7 t2 + 2t10 t2 + 2t10 t5 + t13 t8 2t4 + t12 t + t9 2t4 + t12 t6 t6 t3 + t11 2t3 + 2t11 t + 3t9 4t7 3t5 + t13 4t7 3t5 + t13 2t3 + 2t11 t + 3t9 t4 t2 t6 1

Exceptional hyperplanes

Unknown