The representation theory of the restricted rational Cherednik algebra for G13

Computed by Ulrich Thiel using CHAMP (see LMS J. Comput. Math., 2015). Last update on Fri Mar 27 12:48:16 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

{ϕ4,3,  ϕ2,7',  ϕ4,5,  ϕ2,1,  ϕ2,5,  ϕ2,7''}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,09611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,69611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,129611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,189611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ2,7'822 + 4t + 2t2
ϕ2,49622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,1822 + 4t + 2t2
ϕ2,5822 + 4t + 2t2
ϕ2,109622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,7''822 + 4t + 2t2
ϕ3,49633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,29633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,89633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,69633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ4,31684 + 8t + 4t2
ϕ4,51684 + 8t + 4t2

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0
ϕ1,6 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0
ϕ1,12 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0
ϕ1,18 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0
ϕ2,7' 2 2 2 2 1 2 0 1 2 0 2 2 2 2 0 0
ϕ2,4 2 2 2 2 0 2 0 0 2 0 2 2 2 2 0 1
ϕ2,1 2 2 2 2 0 2 1 0 2 1 2 2 2 2 0 0
ϕ2,5 2 2 2 2 1 2 0 1 2 0 2 2 2 2 0 0
ϕ2,10 2 2 2 2 0 2 0 0 2 0 2 2 2 2 1 0
ϕ2,7'' 2 2 2 2 0 2 1 0 2 1 2 2 2 2 0 0
ϕ3,4 3 3 3 3 0 3 0 1 3 0 3 3 3 3 0 1
ϕ3,2 3 3 3 3 0 3 0 0 3 1 3 3 3 3 1 0
ϕ3,8 3 3 3 3 0 3 1 0 3 0 3 3 3 3 0 1
ϕ3,6 3 3 3 3 1 3 0 0 3 0 3 3 3 3 1 0
ϕ4,3 4 4 4 4 0 4 0 0 4 0 4 4 4 4 1 1
ϕ4,5 4 4 4 4 0 4 0 0 4 0 4 4 4 4 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 t6 t12 t18 0 t4 t 0 t10 0 t4 t2 t8 t6 0 0
ϕ1,6 t6 1 t18 t12 t t10 0 0 t4 0 t2 t4 t6 t8 0 0
ϕ1,12 t12 t18 1 t6 0 t4 0 t t10 0 t8 t6 t4 t2 0 0
ϕ1,18 t18 t12 t6 1 0 t10 0 0 t4 t t6 t8 t2 t4 0 0
ϕ2,7' t5 + t13 t7 + t11 t + t17 t7 + t11 1 t5 + t9 0 t2 t3 + t11 0 t + t9 t3 + t7 2t5 t3 + t7 0 0
ϕ2,4 t4 + t8 t10 + t14 t4 + t8 t10 + t14 0 1 + t8 0 0 t6 + t14 0 t4 + t8 t2 + t6 t4 + t8 t2 + t6 0 t
ϕ2,1 t7 + t11 t5 + t13 t7 + t11 t + t17 0 t3 + t11 1 0 t5 + t9 t2 t3 + t7 t + t9 t3 + t7 2t5 0 0
ϕ2,5 t7 + t11 t + t17 t7 + t11 t5 + t13 t2 t3 + t11 0 1 t5 + t9 0 t3 + t7 2t5 t3 + t7 t + t9 0 0
ϕ2,10 t10 + t14 t4 + t8 t10 + t14 t4 + t8 0 t6 + t14 0 0 1 + t8 0 t2 + t6 t4 + t8 t2 + t6 t4 + t8 t 0
ϕ2,7'' t + t17 t7 + t11 t5 + t13 t7 + t11 0 t5 + t9 t2 0 t3 + t11 1 2t5 t3 + t7 t + t9 t3 + t7 0 0
ϕ3,4 t4 + t8 + t12 t2 + t6 + t10 t8 + t12 + t16 t6 + t10 + t14 0 t4 + t8 + t12 0 t t2 + t6 + t10 0 1 + t4 + t8 t2 + 2t6 2t4 + t8 t2 + t6 + t10 0 t
ϕ3,2 t2 + t6 + t10 t4 + t8 + t12 t6 + t10 + t14 t8 + t12 + t16 0 t2 + t6 + t10 0 0 t4 + t8 + t12 t t2 + 2t6 1 + t4 + t8 t2 + t6 + t10 2t4 + t8 t 0
ϕ3,8 t8 + t12 + t16 t6 + t10 + t14 t4 + t8 + t12 t2 + t6 + t10 0 t4 + t8 + t12 t 0 t2 + t6 + t10 0 2t4 + t8 t2 + t6 + t10 1 + t4 + t8 t2 + 2t6 0 t
ϕ3,6 t6 + t10 + t14 t8 + t12 + t16 t2 + t6 + t10 t4 + t8 + t12 t t2 + t6 + t10 0 0 t4 + t8 + t12 0 t2 + t6 + t10 2t4 + t8 t2 + 2t6 1 + t4 + t8 t 0
ϕ4,3 t5 + 2t9 + t13 t3 + t7 + t11 + t15 t5 + 2t9 + t13 t3 + t7 + t11 + t15 0 t + t5 + t9 + t13 0 0 t3 + 2t7 + t11 0 t + 2t5 + t9 2t3 + 2t7 t + 2t5 + t9 2t3 + 2t7 1 t2
ϕ4,5 t3 + t7 + t11 + t15 t5 + 2t9 + t13 t3 + t7 + t11 + t15 t5 + 2t9 + t13 0 t3 + 2t7 + t11 0 0 t + t5 + t9 + t13 0 2t3 + 2t7 t + 2t5 + t9 2t3 + 2t7 t + 2t5 + t9 t2 1

Exceptional hyperplanes

k2,1
k1,1
k1,1 − 2k2,1
k1,1 − k2,1
k1,1 + k2,1
k1,1 + 2k2,1

For the generic point of the hyperplane k2,1

Quick navigation: Exceptional hyperplanes, For generic parameters

Non-singleton Calogero–Moser families

{ϕ1,0,  ϕ1,12,  ϕ2,4},   {ϕ1,6,  ϕ1,18,  ϕ2,10},   {ϕ3,4,  ϕ3,8},   {ϕ3,2,  ϕ3,6},   {ϕ4,3,  ϕ2,7',  ϕ4,5,  ϕ2,1,  ϕ2,5,  ϕ2,7''}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,01611 + 2t + 3t2 + 4t3 + 3t4 + 2t5 + t6
ϕ1,61611 + 2t + 3t2 + 4t3 + 3t4 + 2t5 + t6
ϕ1,121611 + 2t + 3t2 + 4t3 + 3t4 + 2t5 + t6
ϕ1,181611 + 2t + 3t2 + 4t3 + 3t4 + 2t5 + t6
ϕ2,7'822 + 4t + 2t2
ϕ2,43242 + 4t + 6t2 + 8t3 + 6t4 + 4t5 + 2t6
ϕ2,1822 + 4t + 2t2
ϕ2,5822 + 4t + 2t2
ϕ2,103242 + 4t + 6t2 + 8t3 + 6t4 + 4t5 + 2t6
ϕ2,7''822 + 4t + 2t2
ϕ3,44833 + 6t + 9t2 + 12t3 + 9t4 + 6t5 + 3t6
ϕ3,24833 + 6t + 9t2 + 12t3 + 9t4 + 6t5 + 3t6
ϕ3,84833 + 6t + 9t2 + 12t3 + 9t4 + 6t5 + 3t6
ϕ3,64833 + 6t + 9t2 + 12t3 + 9t4 + 6t5 + 3t6
ϕ4,31684 + 8t + 4t2
ϕ4,51684 + 8t + 4t2

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0
ϕ1,6 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0
ϕ1,12 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0
ϕ1,18 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0
ϕ2,7' 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 0
ϕ2,4 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1
ϕ2,1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0
ϕ2,5 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0
ϕ2,10 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0
ϕ2,7'' 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0
ϕ3,4 1 1 0 0 0 1 0 1 1 0 2 2 1 1 0 1
ϕ3,2 1 1 0 0 0 1 0 0 1 1 2 2 1 1 1 0
ϕ3,8 0 0 1 1 0 1 1 0 1 0 1 1 2 2 0 1
ϕ3,6 0 0 1 1 1 1 0 0 1 0 1 1 2 2 1 0
ϕ4,3 0 1 0 1 0 2 0 0 1 0 2 2 2 2 1 1
ϕ4,5 1 0 1 0 0 1 0 0 2 0 2 2 2 2 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 t6 0 0 0 0 t 0 0 0 t4 t2 0 0 0 0
ϕ1,6 t6 1 0 0 t 0 0 0 0 0 t2 t4 0 0 0 0
ϕ1,12 0 0 1 t6 0 0 0 t 0 0 0 0 t4 t2 0 0
ϕ1,18 0 0 t6 1 0 0 0 0 0 t 0 0 t2 t4 0 0
ϕ2,7' t5 0 t 0 1 0 0 t2 t3 0 t t3 t5 t3 0 0
ϕ2,4 0 0 0 0 0 1 0 0 t6 0 t4 t2 t4 t2 0 t
ϕ2,1 0 t5 0 t 0 t3 1 0 0 t2 t3 t t3 t5 0 0
ϕ2,5 0 t 0 t5 t2 t3 0 1 0 0 t3 t5 t3 t 0 0
ϕ2,10 0 0 0 0 0 t6 0 0 1 0 t2 t4 t2 t4 t 0
ϕ2,7'' t 0 t5 0 0 0 t2 0 t3 1 t5 t3 t t3 0 0
ϕ3,4 t4 t2 0 0 0 t4 0 t t2 0 1 + t4 t2 + t6 t4 t2 0 t
ϕ3,2 t2 t4 0 0 0 t2 0 0 t4 t t2 + t6 1 + t4 t2 t4 t 0
ϕ3,8 0 0 t4 t2 0 t4 t 0 t2 0 t4 t2 1 + t4 t2 + t6 0 t
ϕ3,6 0 0 t2 t4 t t2 0 0 t4 0 t2 t4 t2 + t6 1 + t4 t 0
ϕ4,3 0 t3 0 t3 0 t + t5 0 0 t3 0 t + t5 2t3 t + t5 2t3 1 t2
ϕ4,5 t3 0 t3 0 0 t3 0 0 t + t5 0 2t3 t + t5 2t3 t + t5 t2 1

For the generic point of the hyperplane k1,1

Quick navigation: Exceptional hyperplanes, For generic parameters

Non-singleton Calogero–Moser families

{ϕ3,4,  ϕ3,2},   {ϕ4,3,  ϕ2,7',  ϕ4,5,  ϕ2,4,  ϕ2,1,  ϕ2,5,  ϕ2,10,  ϕ2,7''},   {ϕ1,0,  ϕ1,6},   {ϕ1,12,  ϕ1,18},   {ϕ3,8,  ϕ3,6}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,04811 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 6t6 + 6t7 + 5t8 + 4t9 + 3t10 + 2t11 + t12
ϕ1,64811 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 6t6 + 6t7 + 5t8 + 4t9 + 3t10 + 2t11 + t12
ϕ1,124811 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 6t6 + 6t7 + 5t8 + 4t9 + 3t10 + 2t11 + t12
ϕ1,184811 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 6t6 + 6t7 + 5t8 + 4t9 + 3t10 + 2t11 + t12
ϕ2,7'822 + 4t + 2t2
ϕ2,4242
ϕ2,1822 + 4t + 2t2
ϕ2,5822 + 4t + 2t2
ϕ2,10242
ϕ2,7''822 + 4t + 2t2
ϕ3,44833 + 6t + 6t2 + 6t3 + 6t4 + 6t5 + 6t6 + 6t7 + 3t8
ϕ3,24833 + 6t + 6t2 + 6t3 + 6t4 + 6t5 + 6t6 + 6t7 + 3t8
ϕ3,84833 + 6t + 6t2 + 6t3 + 6t4 + 6t5 + 6t6 + 6t7 + 3t8
ϕ3,64833 + 6t + 6t2 + 6t3 + 6t4 + 6t5 + 6t6 + 6t7 + 3t8
ϕ4,31484 + 6t + 4t2
ϕ4,51484 + 6t + 4t2

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0
ϕ1,6 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0
ϕ1,12 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0
ϕ1,18 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0
ϕ2,7' 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0
ϕ2,4 2 0 2 0 0 1 0 0 0 0 0 2 0 2 0 0
ϕ2,1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0
ϕ2,5 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0
ϕ2,10 0 2 0 2 0 0 0 0 1 0 2 0 2 0 0 0
ϕ2,7'' 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0
ϕ3,4 1 2 1 2 0 0 0 1 0 0 2 1 2 1 0 1
ϕ3,2 2 1 2 1 0 0 0 0 0 1 1 2 1 2 1 0
ϕ3,8 1 2 1 2 0 0 1 0 0 0 2 1 2 1 0 1
ϕ3,6 2 1 2 1 1 0 0 0 0 0 1 2 1 2 1 0
ϕ4,3 2 2 2 2 0 0 0 0 0 0 2 2 2 2 1 1
ϕ4,5 2 2 2 2 0 0 0 0 0 0 2 2 2 2 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 0 t12 0 0 0 t 0 0 0 0 t2 0 t6 0 0
ϕ1,6 0 1 0 t12 t 0 0 0 0 0 t2 0 t6 0 0 0
ϕ1,12 t12 0 1 0 0 0 0 t 0 0 0 t6 0 t2 0 0
ϕ1,18 0 t12 0 1 0 0 0 0 0 t t6 0 t2 0 0 0
ϕ2,7' t5 t7 t t11 1 0 0 t2 0 0 t t7 t5 t3 0 0
ϕ2,4 t4 + t8 0 t4 + t8 0 0 1 0 0 0 0 0 t2 + t6 0 t2 + t6 0 0
ϕ2,1 t7 t5 t11 t 0 0 1 0 0 t2 t7 t t3 t5 0 0
ϕ2,5 t11 t t7 t5 t2 0 0 1 0 0 t3 t5 t7 t 0 0
ϕ2,10 0 t4 + t8 0 t4 + t8 0 0 0 0 1 0 t2 + t6 0 t2 + t6 0 0 0
ϕ2,7'' t t11 t5 t7 0 0 t2 0 0 1 t5 t3 t t7 0 0
ϕ3,4 t4 t2 + t6 t8 t6 + t10 0 0 0 t 0 0 1 + t4 t6 t4 + t8 t2 0 t
ϕ3,2 t2 + t6 t4 t6 + t10 t8 0 0 0 0 0 t t6 1 + t4 t2 t4 + t8 t 0
ϕ3,8 t8 t6 + t10 t4 t2 + t6 0 0 t 0 0 0 t4 + t8 t2 1 + t4 t6 0 t
ϕ3,6 t6 + t10 t8 t2 + t6 t4 t 0 0 0 0 0 t2 t4 + t8 t6 1 + t4 t 0
ϕ4,3 t5 + t9 t3 + t7 t5 + t9 t3 + t7 0 0 0 0 0 0 t + t5 t3 + t7 t + t5 t3 + t7 1 t2
ϕ4,5 t3 + t7 t5 + t9 t3 + t7 t5 + t9 0 0 0 0 0 0 t3 + t7 t + t5 t3 + t7 t + t5 t2 1

For the generic point of the hyperplane k1,1 − 2k2,1

Quick navigation: Exceptional hyperplanes, For generic parameters

Non-singleton Calogero–Moser families

{ϕ3,4,  ϕ1,6,  ϕ1,12,  ϕ3,6,  ϕ4,3,  ϕ2,7',  ϕ4,5,  ϕ2,1,  ϕ2,5,  ϕ2,7''}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,09611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,6111
ϕ1,12111
ϕ1,189611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ2,7'242
ϕ2,49622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,1822 + 4t + 2t2
ϕ2,5242
ϕ2,109622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,7''822 + 4t + 2t2
ϕ3,4393
ϕ3,29633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,89633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,6393
ϕ4,31384 + 5t + 4t2
ϕ4,51384 + 5t + 4t2

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0
ϕ1,6 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0
ϕ1,12 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0
ϕ1,18 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0
ϕ2,7' 2 0 0 2 1 2 0 0 2 0 0 2 2 0 0 0
ϕ2,4 2 0 0 2 0 2 0 0 2 0 0 2 2 0 0 1
ϕ2,1 2 0 0 2 0 2 1 0 2 1 0 2 2 0 0 0
ϕ2,5 2 0 0 2 0 2 0 1 2 0 0 2 2 0 0 0
ϕ2,10 2 0 0 2 0 2 0 0 2 0 0 2 2 0 1 0
ϕ2,7'' 2 0 0 2 0 2 1 0 2 1 0 2 2 0 0 0
ϕ3,4 3 0 0 3 0 3 0 0 3 0 1 3 3 0 0 0
ϕ3,2 3 0 0 3 0 3 0 0 3 1 0 3 3 0 1 0
ϕ3,8 3 0 0 3 0 3 1 0 3 0 0 3 3 0 0 1
ϕ3,6 3 0 0 3 0 3 0 0 3 0 0 3 3 1 0 0
ϕ4,3 4 0 0 4 0 4 0 0 4 0 0 4 4 0 1 1
ϕ4,5 4 0 0 4 0 4 0 0 4 0 0 4 4 0 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 0 0 t18 0 t4 t 0 t10 0 0 t2 t8 0 0 0
ϕ1,6 t6 1 0 t12 0 t10 0 0 t4 0 0 t4 t6 0 0 0
ϕ1,12 t12 0 1 t6 0 t4 0 0 t10 0 0 t6 t4 0 0 0
ϕ1,18 t18 0 0 1 0 t10 0 0 t4 t 0 t8 t2 0 0 0
ϕ2,7' t5 + t13 0 0 t7 + t11 1 t5 + t9 0 0 t3 + t11 0 0 t3 + t7 2t5 0 0 0
ϕ2,4 t4 + t8 0 0 t10 + t14 0 1 + t8 0 0 t6 + t14 0 0 t2 + t6 t4 + t8 0 0 t
ϕ2,1 t7 + t11 0 0 t + t17 0 t3 + t11 1 0 t5 + t9 t2 0 t + t9 t3 + t7 0 0 0
ϕ2,5 t7 + t11 0 0 t5 + t13 0 t3 + t11 0 1 t5 + t9 0 0 2t5 t3 + t7 0 0 0
ϕ2,10 t10 + t14 0 0 t4 + t8 0 t6 + t14 0 0 1 + t8 0 0 t4 + t8 t2 + t6 0 t 0
ϕ2,7'' t + t17 0 0 t7 + t11 0 t5 + t9 t2 0 t3 + t11 1 0 t3 + t7 t + t9 0 0 0
ϕ3,4 t4 + t8 + t12 0 0 t6 + t10 + t14 0 t4 + t8 + t12 0 0 t2 + t6 + t10 0 1 t2 + 2t6 2t4 + t8 0 0 0
ϕ3,2 t2 + t6 + t10 0 0 t8 + t12 + t16 0 t2 + t6 + t10 0 0 t4 + t8 + t12 t 0 1 + t4 + t8 t2 + t6 + t10 0 t 0
ϕ3,8 t8 + t12 + t16 0 0 t2 + t6 + t10 0 t4 + t8 + t12 t 0 t2 + t6 + t10 0 0 t2 + t6 + t10 1 + t4 + t8 0 0 t
ϕ3,6 t6 + t10 + t14 0 0 t4 + t8 + t12 0 t2 + t6 + t10 0 0 t4 + t8 + t12 0 0 2t4 + t8 t2 + 2t6 1 0 0
ϕ4,3 t5 + 2t9 + t13 0 0 t3 + t7 + t11 + t15 0 t + t5 + t9 + t13 0 0 t3 + 2t7 + t11 0 0 2t3 + 2t7 t + 2t5 + t9 0 1 t2
ϕ4,5 t3 + t7 + t11 + t15 0 0 t5 + 2t9 + t13 0 t3 + 2t7 + t11 0 0 t + t5 + t9 + t13 0 0 t + 2t5 + t9 2t3 + 2t7 0 t2 1

For the generic point of the hyperplane k1,1 − k2,1

Quick navigation: Exceptional hyperplanes, For generic parameters

Non-singleton Calogero–Moser families

{ϕ3,8,  ϕ1,12,  ϕ2,10},   {ϕ3,2,  ϕ1,6,  ϕ2,4},   {ϕ4,3,  ϕ2,7',  ϕ4,5,  ϕ2,1,  ϕ2,5,  ϕ2,7''}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,09611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,61211 + 2t + 3t2 + 4t3 + 2t4
ϕ1,121211 + 2t + 3t2 + 4t3 + 2t4
ϕ1,189611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ2,7'822 + 4t + 2t2
ϕ2,41222 + 4t + 3t2 + 2t3 + t4
ϕ2,1822 + 4t + 2t2
ϕ2,5822 + 4t + 2t2
ϕ2,101222 + 4t + 3t2 + 2t3 + t4
ϕ2,7''822 + 4t + 2t2
ϕ3,49633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,27233 + 6t + 7t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 7t8 + 6t9 + 3t10
ϕ3,87233 + 6t + 7t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 7t8 + 6t9 + 3t10
ϕ3,69633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ4,31684 + 8t + 4t2
ϕ4,51684 + 8t + 4t2

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0
ϕ1,6 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0
ϕ1,12 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0
ϕ1,18 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0
ϕ2,7' 2 0 1 2 1 0 0 1 1 0 2 2 0 2 0 0
ϕ2,4 2 0 1 2 0 1 0 0 0 0 2 1 1 2 0 1
ϕ2,1 2 0 0 2 0 0 1 0 0 1 2 2 2 2 0 0
ϕ2,5 2 1 0 2 1 1 0 1 0 0 2 0 2 2 0 0
ϕ2,10 2 1 0 2 0 0 0 0 1 0 2 1 1 2 1 0
ϕ2,7'' 2 0 0 2 0 0 1 0 0 1 2 2 2 2 0 0
ϕ3,4 3 1 0 3 0 0 0 1 1 0 3 2 2 3 0 1
ϕ3,2 3 0 0 3 0 0 0 0 0 1 3 3 3 3 1 0
ϕ3,8 3 0 0 3 0 0 1 0 0 0 3 3 3 3 0 1
ϕ3,6 3 0 1 3 1 1 0 0 0 0 3 2 2 3 1 0
ϕ4,3 4 1 0 4 0 1 0 0 0 0 4 2 4 4 1 1
ϕ4,5 4 0 1 4 0 0 0 0 1 0 4 4 2 4 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 0 0 t18 0 0 t 0 0 0 t4 t2 t8 t6 0 0
ϕ1,6 t6 1 0 t12 t 0 0 0 t4 0 t2 0 0 t8 0 0
ϕ1,12 t12 0 1 t6 0 t4 0 t 0 0 t8 0 0 t2 0 0
ϕ1,18 t18 0 0 1 0 0 0 0 0 t t6 t8 t2 t4 0 0
ϕ2,7' t5 + t13 0 t t7 + t11 1 0 0 t2 t3 0 t + t9 t3 + t7 0 t3 + t7 0 0
ϕ2,4 t4 + t8 0 t4 t10 + t14 0 1 0 0 0 0 t4 + t8 t6 t4 t2 + t6 0 t
ϕ2,1 t7 + t11 0 0 t + t17 0 0 1 0 0 t2 t3 + t7 t + t9 t3 + t7 2t5 0 0
ϕ2,5 t7 + t11 t 0 t5 + t13 t2 t3 0 1 0 0 t3 + t7 0 t3 + t7 t + t9 0 0
ϕ2,10 t10 + t14 t4 0 t4 + t8 0 0 0 0 1 0 t2 + t6 t4 t6 t4 + t8 t 0
ϕ2,7'' t + t17 0 0 t7 + t11 0 0 t2 0 0 1 2t5 t3 + t7 t + t9 t3 + t7 0 0
ϕ3,4 t4 + t8 + t12 t2 0 t6 + t10 + t14 0 0 0 t t2 0 1 + t4 + t8 t2 + t6 t4 + t8 t2 + t6 + t10 0 t
ϕ3,2 t2 + t6 + t10 0 0 t8 + t12 + t16 0 0 0 0 0 t t2 + 2t6 1 + t4 + t8 t2 + t6 + t10 2t4 + t8 t 0
ϕ3,8 t8 + t12 + t16 0 0 t2 + t6 + t10 0 0 t 0 0 0 2t4 + t8 t2 + t6 + t10 1 + t4 + t8 t2 + 2t6 0 t
ϕ3,6 t6 + t10 + t14 0 t2 t4 + t8 + t12 t t2 0 0 0 0 t2 + t6 + t10 t4 + t8 t2 + t6 1 + t4 + t8 t 0
ϕ4,3 t5 + 2t9 + t13 t3 0 t3 + t7 + t11 + t15 0 t 0 0 0 0 t + 2t5 + t9 t3 + t7 t + 2t5 + t9 2t3 + 2t7 1 t2
ϕ4,5 t3 + t7 + t11 + t15 0 t3 t5 + 2t9 + t13 0 0 0 0 t 0 2t3 + 2t7 t + 2t5 + t9 t3 + t7 t + 2t5 + t9 t2 1

For the generic point of the hyperplane k1,1 + k2,1

Quick navigation: Exceptional hyperplanes, For generic parameters

Non-singleton Calogero–Moser families

{ϕ3,4,  ϕ1,0,  ϕ2,10},   {ϕ3,6,  ϕ1,18,  ϕ2,4},   {ϕ4,3,  ϕ2,7',  ϕ4,5,  ϕ2,1,  ϕ2,5,  ϕ2,7''}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,01211 + 2t + 3t2 + 4t3 + 2t4
ϕ1,69611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,129611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,181211 + 2t + 3t2 + 4t3 + 2t4
ϕ2,7'822 + 4t + 2t2
ϕ2,41222 + 4t + 3t2 + 2t3 + t4
ϕ2,1822 + 4t + 2t2
ϕ2,5822 + 4t + 2t2
ϕ2,101222 + 4t + 3t2 + 2t3 + t4
ϕ2,7''822 + 4t + 2t2
ϕ3,47233 + 6t + 7t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 7t8 + 6t9 + 3t10
ϕ3,29633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,89633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,67233 + 6t + 7t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 7t8 + 6t9 + 3t10
ϕ4,31684 + 8t + 4t2
ϕ4,51684 + 8t + 4t2

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0
ϕ1,6 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0
ϕ1,12 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0
ϕ1,18 0 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0
ϕ2,7' 0 2 2 0 1 0 0 1 0 0 2 2 2 2 0 0
ϕ2,4 1 2 2 0 0 1 0 0 0 0 1 2 2 1 0 1
ϕ2,1 0 2 2 1 0 1 1 0 0 1 2 2 2 0 0 0
ϕ2,5 0 2 2 0 1 0 0 1 0 0 2 2 2 2 0 0
ϕ2,10 0 2 2 1 0 0 0 0 1 0 1 2 2 1 1 0
ϕ2,7'' 1 2 2 0 0 0 1 0 1 1 0 2 2 2 0 0
ϕ3,4 0 3 3 0 0 0 0 1 0 0 3 3 3 3 0 1
ϕ3,2 1 3 3 0 0 1 0 0 0 1 2 3 3 2 1 0
ϕ3,8 0 3 3 1 0 0 1 0 1 0 2 3 3 2 0 1
ϕ3,6 0 3 3 0 1 0 0 0 0 0 3 3 3 3 1 0
ϕ4,3 0 4 4 1 0 1 0 0 0 0 4 4 4 2 1 1
ϕ4,5 1 4 4 0 0 0 0 0 1 0 2 4 4 4 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 t6 t12 0 0 t4 t 0 0 0 0 t2 t8 0 0 0
ϕ1,6 0 1 t18 0 t 0 0 0 0 0 t2 t4 t6 t8 0 0
ϕ1,12 0 t18 1 0 0 0 0 t 0 0 t8 t6 t4 t2 0 0
ϕ1,18 0 t12 t6 1 0 0 0 0 t4 t 0 t8 t2 0 0 0
ϕ2,7' 0 t7 + t11 t + t17 0 1 0 0 t2 0 0 t + t9 t3 + t7 2t5 t3 + t7 0 0
ϕ2,4 t4 t10 + t14 t4 + t8 0 0 1 0 0 0 0 t4 t2 + t6 t4 + t8 t6 0 t
ϕ2,1 0 t5 + t13 t7 + t11 t 0 t3 1 0 0 t2 t3 + t7 t + t9 t3 + t7 0 0 0
ϕ2,5 0 t + t17 t7 + t11 0 t2 0 0 1 0 0 t3 + t7 2t5 t3 + t7 t + t9 0 0
ϕ2,10 0 t4 + t8 t10 + t14 t4 0 0 0 0 1 0 t6 t4 + t8 t2 + t6 t4 t 0
ϕ2,7'' t t7 + t11 t5 + t13 0 0 0 t2 0 t3 1 0 t3 + t7 t + t9 t3 + t7 0 0
ϕ3,4 0 t2 + t6 + t10 t8 + t12 + t16 0 0 0 0 t 0 0 1 + t4 + t8 t2 + 2t6 2t4 + t8 t2 + t6 + t10 0 t
ϕ3,2 t2 t4 + t8 + t12 t6 + t10 + t14 0 0 t2 0 0 0 t t2 + t6 1 + t4 + t8 t2 + t6 + t10 t4 + t8 t 0
ϕ3,8 0 t6 + t10 + t14 t4 + t8 + t12 t2 0 0 t 0 t2 0 t4 + t8 t2 + t6 + t10 1 + t4 + t8 t2 + t6 0 t
ϕ3,6 0 t8 + t12 + t16 t2 + t6 + t10 0 t 0 0 0 0 0 t2 + t6 + t10 2t4 + t8 t2 + 2t6 1 + t4 + t8 t 0
ϕ4,3 0 t3 + t7 + t11 + t15 t5 + 2t9 + t13 t3 0 t 0 0 0 0 t + 2t5 + t9 2t3 + 2t7 t + 2t5 + t9 t3 + t7 1 t2
ϕ4,5 t3 t5 + 2t9 + t13 t3 + t7 + t11 + t15 0 0 0 0 0 t 0 t3 + t7 t + 2t5 + t9 2t3 + 2t7 t + 2t5 + t9 t2 1

For the generic point of the hyperplane k1,1 + 2k2,1

Quick navigation: Exceptional hyperplanes, For generic parameters

Non-singleton Calogero–Moser families

{ϕ1,0,  ϕ1,18,  ϕ2,7',  ϕ2,1,  ϕ2,5,  ϕ2,7'',  ϕ3,2,  ϕ3,8,  ϕ4,3,  ϕ4,5}

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

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,0111
ϕ1,69611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,129611 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 7t12 + 6t13 + 5t14 + 4t15 + 3t16 + 2t17 + t18
ϕ1,18111
ϕ2,7'822 + 4t + 2t2
ϕ2,49622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,1242
ϕ2,5822 + 4t + 2t2
ϕ2,109622 + 4t + 6t2 + 8t3 + 8t4 + 8t5 + 8t6 + 8t7 + 8t8 + 8t9 + 8t10 + 8t11 + 6t12 + 4t13 + 2t14
ϕ2,7''242
ϕ3,49633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ3,2393
ϕ3,8393
ϕ3,69633 + 6t + 9t2 + 12t3 + 12t4 + 12t5 + 12t6 + 12t7 + 9t8 + 6t9 + 3t10
ϕ4,31384 + 5t + 4t2
ϕ4,51384 + 5t + 4t2

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0
ϕ1,6 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0
ϕ1,12 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0
ϕ1,18 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0
ϕ2,7' 0 2 2 0 1 2 0 1 2 0 2 0 0 2 0 0
ϕ2,4 0 2 2 0 0 2 0 0 2 0 2 0 0 2 0 1
ϕ2,1 0 2 2 0 0 2 1 0 2 0 2 0 0 2 0 0
ϕ2,5 0 2 2 0 1 2 0 1 2 0 2 0 0 2 0 0
ϕ2,10 0 2 2 0 0 2 0 0 2 0 2 0 0 2 1 0
ϕ2,7'' 0 2 2 0 0 2 0 0 2 1 2 0 0 2 0 0
ϕ3,4 0 3 3 0 0 3 0 1 3 0 3 0 0 3 0 1
ϕ3,2 0 3 3 0 0 3 0 0 3 0 3 1 0 3 0 0
ϕ3,8 0 3 3 0 0 3 0 0 3 0 3 0 1 3 0 0
ϕ3,6 0 3 3 0 1 3 0 0 3 0 3 0 0 3 1 0
ϕ4,3 0 4 4 0 0 4 0 0 4 0 4 0 0 4 1 1
ϕ4,5 0 4 4 0 0 4 0 0 4 0 4 0 0 4 1 1

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,6) L(ϕ1,12) L(ϕ1,18) L(ϕ2,7') L(ϕ2,4) L(ϕ2,1) L(ϕ2,5) L(ϕ2,10) L(ϕ2,7'') L(ϕ3,4) L(ϕ3,2) L(ϕ3,8) L(ϕ3,6) L(ϕ4,3) L(ϕ4,5)
ϕ1,0 1 t6 t12 0 0 t4 0 0 t10 0 t4 0 0 t6 0 0
ϕ1,6 0 1 t18 0 t t10 0 0 t4 0 t2 0 0 t8 0 0
ϕ1,12 0 t18 1 0 0 t4 0 t t10 0 t8 0 0 t2 0 0
ϕ1,18 0 t12 t6 1 0 t10 0 0 t4 0 t6 0 0 t4 0 0
ϕ2,7' 0 t7 + t11 t + t17 0 1 t5 + t9 0 t2 t3 + t11 0 t + t9 0 0 t3 + t7 0 0
ϕ2,4 0 t10 + t14 t4 + t8 0 0 1 + t8 0 0 t6 + t14 0 t4 + t8 0 0 t2 + t6 0 t
ϕ2,1 0 t5 + t13 t7 + t11 0 0 t3 + t11 1 0 t5 + t9 0 t3 + t7 0 0 2t5 0 0
ϕ2,5 0 t + t17 t7 + t11 0 t2 t3 + t11 0 1 t5 + t9 0 t3 + t7 0 0 t + t9 0 0
ϕ2,10 0 t4 + t8 t10 + t14 0 0 t6 + t14 0 0 1 + t8 0 t2 + t6 0 0 t4 + t8 t 0
ϕ2,7'' 0 t7 + t11 t5 + t13 0 0 t5 + t9 0 0 t3 + t11 1 2t5 0 0 t3 + t7 0 0
ϕ3,4 0 t2 + t6 + t10 t8 + t12 + t16 0 0 t4 + t8 + t12 0 t t2 + t6 + t10 0 1 + t4 + t8 0 0 t2 + t6 + t10 0 t
ϕ3,2 0 t4 + t8 + t12 t6 + t10 + t14 0 0 t2 + t6 + t10 0 0 t4 + t8 + t12 0 t2 + 2t6 1 0 2t4 + t8 0 0
ϕ3,8 0 t6 + t10 + t14 t4 + t8 + t12 0 0 t4 + t8 + t12 0 0 t2 + t6 + t10 0 2t4 + t8 0 1 t2 + 2t6 0 0
ϕ3,6 0 t8 + t12 + t16 t2 + t6 + t10 0 t t2 + t6 + t10 0 0 t4 + t8 + t12 0 t2 + t6 + t10 0 0 1 + t4 + t8 t 0
ϕ4,3 0 t3 + t7 + t11 + t15 t5 + 2t9 + t13 0 0 t + t5 + t9 + t13 0 0 t3 + 2t7 + t11 0 t + 2t5 + t9 0 0 2t3 + 2t7 1 t2
ϕ4,5 0 t5 + 2t9 + t13 t3 + t7 + t11 + t15 0 0 t3 + 2t7 + t11 0 0 t + t5 + t9 + t13 0 2t3 + 2t7 0 0 t + 2t5 + t9 t2 1