[Back to overview]

SL6(q) for q = 4 mod 6


Labels of unipotent almost characters:
  1:  [ 1, 1, 1, 1, 1, 1 ]
  2:  [ 2, 1, 1, 1, 1 ]
  3:  [ 2, 2, 1, 1 ]
  4:  [ 2, 2, 2 ]
  5:  [ 3, 1, 1, 1 ]
  6:  [ 3, 2, 1 ]
  7:  [ 3, 3 ]
  8:  [ 4, 1, 1 ]
  9:  [ 4, 2 ]
 10:  [ 5, 1 ]
 11:  [ 6 ]

In row "i,j,k:" we give the scalar product of the tensor product of almost 
characters i and j with almost character k, if this is nonzero and i >= j.
1, 1, 1:    3*q^10+3*q^8+3*q^7+7*q^6+3*q^5+10*q^4+5*q^3+7*q^2+6*q+1
1, 1, 2:    3*q^9+3*q^8+6*q^7+10*q^6+13*q^5+14*q^4+23*q^3+19*q^2+20*q+7
1, 1, 3:    3*q^8+3*q^7+9*q^6+10*q^5+20*q^4+19*q^3+27*q^2+25*q+13
1, 1, 4:    3*q^7+6*q^5+7*q^4+10*q^3+12*q^2+14*q+7
1, 1, 5:    3*q^7+3*q^6+10*q^5+10*q^4+19*q^3+17*q^2+27*q+14
1, 1, 6:    3*q^6+6*q^5+10*q^4+17*q^3+24*q^2+28*q+24
1, 1, 7:    3*q^4+7*q^2+5*q+7
1, 1, 8:    3*q^4+4*q^3+8*q^2+10*q+14
1, 1, 9:    3*q^3+4*q^2+8*q+13
1, 1, 10:    7
1, 1, 11:    1
2, 1, 1:    3*q^9+3*q^8+6*q^7+10*q^6+13*q^5+14*q^4+23*q^3+19*q^2+20*q+7
2, 1, 2:    3*q^8+6*q^7+13*q^6+20*q^5+31*q^4+40*q^3+45*q^2+55*q+28
2, 1, 3:    3*q^7+6*q^6+16*q^5+24*q^4+41*q^3+49*q^2+65*q+42
2, 1, 4:    3*q^6+3*q^5+10*q^4+14*q^3+24*q^2+26*q+21
2, 1, 5:    3*q^6+7*q^5+14*q^4+24*q^3+35*q^2+44*q+42
2, 1, 6:    3*q^5+10*q^4+18*q^3+34*q^2+51*q+54
2, 1, 7:    3*q^3+4*q^2+10*q+14
2, 1, 8:    4*q^3+6*q^2+12*q+26
2, 1, 9:    4*q^2+6*q+19
2, 1, 10:    5
2, 2, 1:    3*q^8+6*q^7+13*q^6+20*q^5+31*q^4+40*q^3+45*q^2+55*q+28
2, 2, 2:    3*q^7+10*q^6+24*q^5+40*q^4+70*q^3+88*q^2+118*q+89
2, 2, 3:    3*q^6+10*q^5+28*q^4+52*q^3+84*q^2+125*q+115
2, 2, 4:    3*q^5+7*q^4+18*q^3+34*q^2+58*q+54
2, 2, 5:    4*q^5+12*q^4+28*q^3+48*q^2+80*q+96
2, 2, 6:    4*q^4+16*q^3+40*q^2+78*q+120
2, 2, 7:    4*q^2+12*q+27
2, 2, 8:    q^3+8*q^2+14*q+42
2, 2, 9:    q^2+8*q+34
2, 2, 10:    8
2, 2, 11:    1
3, 1, 1:    3*q^8+3*q^7+9*q^6+10*q^5+20*q^4+19*q^3+27*q^2+25*q+13
3, 1, 2:    3*q^7+6*q^6+16*q^5+24*q^4+41*q^3+49*q^2+65*q+42
3, 1, 3:    3*q^6+6*q^5+19*q^4+29*q^3+51*q^2+66*q+58
3, 1, 4:    3*q^5+3*q^4+13*q^3+19*q^2+32*q+29
3, 1, 5:    3*q^5+7*q^4+19*q^3+27*q^2+48*q+48
3, 1, 6:    3*q^4+10*q^3+24*q^2+45*q+64
3, 1, 7:    3*q^2+5*q+16
3, 1, 8:    5*q^2+8*q+22
3, 1, 9:    5*q+19
3, 1, 10:    3
3, 2, 1:    3*q^7+6*q^6+16*q^5+24*q^4+41*q^3+49*q^2+65*q+42
3, 2, 2:    3*q^6+10*q^5+28*q^4+52*q^3+84*q^2+125*q+115
3, 2, 3:    3*q^5+10*q^4+34*q^3+65*q^2+123*q+143
3, 2, 4:    3*q^4+7*q^3+24*q^2+48*q+65
3, 2, 5:    4*q^4+14*q^3+37*q^2+72*q+110
3, 2, 6:    4*q^3+20*q^2+60*q+130
3, 2, 7:    6*q+28
3, 2, 8:    2*q^2+12*q+43
3, 2, 9:    2*q+29
3, 2, 10:    6
3, 3, 1:    3*q^6+6*q^5+19*q^4+29*q^3+51*q^2+66*q+58
3, 3, 2:    3*q^5+10*q^4+34*q^3+65*q^2+123*q+143
3, 3, 3:    3*q^4+11*q^3+42*q^2+98*q+161
3, 3, 4:    3*q^3+11*q^2+40*q+76
3, 3, 5:    5*q^3+18*q^2+60*q+120
3, 3, 6:    6*q^2+38*q+132
3, 3, 7:    q+24
3, 3, 8:    q^2+6*q+41
3, 3, 9:    q+30
3, 3, 10:    7
3, 3, 11:    1
4, 1, 1:    3*q^7+6*q^5+7*q^4+10*q^3+12*q^2+14*q+7
4, 1, 2:    3*q^6+3*q^5+10*q^4+14*q^3+24*q^2+26*q+21
4, 1, 3:    3*q^5+3*q^4+13*q^3+19*q^2+32*q+29
4, 1, 4:    3*q^4+10*q^2+10*q+14
4, 1, 5:    3*q^4+4*q^3+12*q^2+21*q+20
4, 1, 6:    3*q^3+7*q^2+18*q+30
4, 1, 7:    3*q+8
4, 1, 8:    6*q+9
4, 1, 9:    8
4, 1, 10:    1
4, 2, 1:    3*q^6+3*q^5+10*q^4+14*q^3+24*q^2+26*q+21
4, 2, 2:    3*q^5+7*q^4+18*q^3+34*q^2+58*q+54
4, 2, 3:    3*q^4+7*q^3+24*q^2+48*q+65
4, 2, 4:    3*q^3+7*q^2+19*q+33
4, 2, 5:    4*q^3+10*q^2+32*q+51
4, 2, 6:    4*q^2+22*q+58
4, 2, 7:    11
4, 2, 8:    3*q+18
4, 2, 9:    14
4, 2, 10:    2
4, 3, 1:    3*q^5+3*q^4+13*q^3+19*q^2+32*q+29
4, 3, 2:    3*q^4+7*q^3+24*q^2+48*q+65
4, 3, 3:    3*q^3+11*q^2+40*q+76
4, 3, 4:    3*q^2+10*q+30
4, 3, 5:    5*q^2+21*q+53
4, 3, 6:    12*q+56
4, 3, 7:    12
4, 3, 8:    2*q+20
4, 3, 9:    9
4, 3, 10:    3
4, 4, 1:    3*q^4+10*q^2+10*q+14
4, 4, 2:    3*q^3+7*q^2+19*q+33
4, 4, 3:    3*q^2+10*q+30
4, 4, 4:    3*q^2+4*q+20
4, 4, 5:    10*q+21
4, 4, 6:    4*q+24
4, 4, 7:    3
4, 4, 8:    q+5
4, 4, 9:    9
4, 4, 10:    2
4, 4, 11:    1
5, 1, 1:    3*q^7+3*q^6+10*q^5+10*q^4+19*q^3+17*q^2+27*q+14
5, 1, 2:    3*q^6+7*q^5+14*q^4+24*q^3+35*q^2+44*q+42
5, 1, 3:    3*q^5+7*q^4+19*q^3+27*q^2+48*q+48
5, 1, 4:    3*q^4+4*q^3+12*q^2+21*q+20
5, 1, 5:    4*q^4+5*q^3+16*q^2+22*q+38
5, 1, 6:    4*q^3+10*q^2+22*q+40
5, 1, 7:    5*q+6
5, 1, 8:    q^2+2*q+10
5, 1, 9:    q+6
5, 2, 1:    3*q^6+7*q^5+14*q^4+24*q^3+35*q^2+44*q+42
5, 2, 2:    4*q^5+12*q^4+28*q^3+48*q^2+80*q+96
5, 2, 3:    4*q^4+14*q^3+37*q^2+72*q+110
5, 2, 4:    4*q^3+10*q^2+32*q+51
5, 2, 5:    q^4+7*q^3+18*q^2+39*q+74
5, 2, 6:    q^3+9*q^2+34*q+86
5, 2, 7:    2*q+19
5, 2, 8:    2*q^2+6*q+24
5, 2, 9:    2*q+18
5, 2, 10:    4
5, 3, 1:    3*q^5+7*q^4+19*q^3+27*q^2+48*q+48
5, 3, 2:    4*q^4+14*q^3+37*q^2+72*q+110
5, 3, 3:    5*q^3+18*q^2+60*q+120
5, 3, 4:    5*q^2+21*q+53
5, 3, 5:    q^3+10*q^2+31*q+86
5, 3, 6:    2*q^2+20*q+90
5, 3, 7:    q+16
5, 3, 8:    4*q+27
5, 3, 9:    18
5, 3, 10:    3
5, 4, 1:    3*q^4+4*q^3+12*q^2+21*q+20
5, 4, 2:    4*q^3+10*q^2+32*q+51
5, 4, 3:    5*q^2+21*q+53
5, 4, 4:    10*q+21
5, 4, 5:    q^2+11*q+40
5, 4, 6:    4*q+40
5, 4, 7:    7
5, 4, 8:    12
5, 4, 9:    7
5, 4, 10:    1
5, 5, 1:    4*q^4+5*q^3+16*q^2+22*q+38
5, 5, 2:    q^4+7*q^3+18*q^2+39*q+74
5, 5, 3:    q^3+10*q^2+31*q+86
5, 5, 4:    q^2+11*q+40
5, 5, 5:    2*q^3+6*q^2+26*q+55
5, 5, 6:    2*q^2+14*q+70
5, 5, 7:    16
5, 5, 8:    q^2+6*q+24
5, 5, 9:    q+19
5, 5, 10:    6
5, 5, 11:    1
6, 1, 1:    3*q^6+6*q^5+10*q^4+17*q^3+24*q^2+28*q+24
6, 1, 2:    3*q^5+10*q^4+18*q^3+34*q^2+51*q+54
6, 1, 3:    3*q^4+10*q^3+24*q^2+45*q+64
6, 1, 4:    3*q^3+7*q^2+18*q+30
6, 1, 5:    4*q^3+10*q^2+22*q+40
6, 1, 6:    4*q^2+18*q+46
6, 1, 7:    10
6, 1, 8:    2*q+8
6, 1, 9:    6
6, 2, 1:    3*q^5+10*q^4+18*q^3+34*q^2+51*q+54
6, 2, 2:    4*q^4+16*q^3+40*q^2+78*q+120
6, 2, 3:    4*q^3+20*q^2+60*q+130
6, 2, 4:    4*q^2+22*q+58
6, 2, 5:    q^3+9*q^2+34*q+86
6, 2, 6:    q^2+17*q+92
6, 2, 7:    16
6, 2, 8:    4*q+24
6, 2, 9:    16
6, 2, 10:    2
6, 3, 1:    3*q^4+10*q^3+24*q^2+45*q+64
6, 3, 2:    4*q^3+20*q^2+60*q+130
6, 3, 3:    6*q^2+38*q+132
6, 3, 4:    12*q+56
6, 3, 5:    2*q^2+20*q+90
6, 3, 6:    8*q+90
6, 3, 7:    16
6, 3, 8:    2*q+28
6, 3, 9:    18
6, 3, 10:    4
6, 4, 1:    3*q^3+7*q^2+18*q+30
6, 4, 2:    4*q^2+22*q+58
6, 4, 3:    12*q+56
6, 4, 4:    4*q+24
6, 4, 5:    4*q+40
6, 4, 6:    2*q+38
6, 4, 7:    6
6, 4, 8:    12
6, 4, 9:    8
6, 4, 10:    2
6, 5, 1:    4*q^3+10*q^2+22*q+40
6, 5, 2:    q^3+9*q^2+34*q+86
6, 5, 3:    2*q^2+20*q+90
6, 5, 4:    4*q+40
6, 5, 5:    2*q^2+14*q+70
6, 5, 6:    6*q+70
6, 5, 7:    12
6, 5, 8:    2*q+26
6, 5, 9:    16
6, 5, 10:    4
6, 6, 1:    4*q^2+18*q+46
6, 6, 2:    q^2+17*q+92
6, 6, 3:    8*q+90
6, 6, 4:    2*q+38
6, 6, 5:    6*q+70
6, 6, 6:    2*q+70
6, 6, 7:    14
6, 6, 8:    q+28
6, 6, 9:    18
6, 6, 10:    6
6, 6, 11:    1
7, 1, 1:    3*q^4+7*q^2+5*q+7
7, 1, 2:    3*q^3+4*q^2+10*q+14
7, 1, 3:    3*q^2+5*q+16
7, 1, 4:    3*q+8
7, 1, 5:    5*q+6
7, 1, 6:    10
7, 1, 7:    2
7, 1, 8:    1
7, 1, 9:    1
7, 2, 1:    3*q^3+4*q^2+10*q+14
7, 2, 2:    4*q^2+12*q+27
7, 2, 3:    6*q+28
7, 2, 4:    11
7, 2, 5:    2*q+19
7, 2, 6:    16
7, 2, 7:    2
7, 2, 8:    4
7, 2, 9:    2
7, 3, 1:    3*q^2+5*q+16
7, 3, 2:    6*q+28
7, 3, 3:    q+24
7, 3, 4:    12
7, 3, 5:    q+16
7, 3, 6:    16
7, 3, 7:    3
7, 3, 8:    5
7, 3, 9:    4
7, 3, 10:    1
7, 4, 1:    3*q+8
7, 4, 2:    11
7, 4, 3:    12
7, 4, 4:    3
7, 4, 5:    7
7, 4, 6:    6
7, 4, 7:    2
7, 4, 8:    3
7, 4, 9:    1
7, 5, 1:    5*q+6
7, 5, 2:    2*q+19
7, 5, 3:    q+16
7, 5, 4:    7
7, 5, 5:    16
7, 5, 6:    12
7, 5, 7:    2
7, 5, 8:    5
7, 5, 9:    2
7, 6, 1:    10
7, 6, 2:    16
7, 6, 3:    16
7, 6, 4:    6
7, 6, 5:    12
7, 6, 6:    14
7, 6, 7:    2
7, 6, 8:    6
7, 6, 9:    4
7, 6, 10:    2
7, 7, 1:    2
7, 7, 2:    2
7, 7, 3:    3
7, 7, 4:    2
7, 7, 5:    2
7, 7, 6:    2
7, 7, 7:    2
7, 7, 8:    1
7, 7, 9:    2
7, 7, 10:    1
7, 7, 11:    1
8, 1, 1:    3*q^4+4*q^3+8*q^2+10*q+14
8, 1, 2:    4*q^3+6*q^2+12*q+26
8, 1, 3:    5*q^2+8*q+22
8, 1, 4:    6*q+9
8, 1, 5:    q^2+2*q+10
8, 1, 6:    2*q+8
8, 1, 7:    1
8, 2, 1:    4*q^3+6*q^2+12*q+26
8, 2, 2:    q^3+8*q^2+14*q+42
8, 2, 3:    2*q^2+12*q+43
8, 2, 4:    3*q+18
8, 2, 5:    2*q^2+6*q+24
8, 2, 6:    4*q+24
8, 2, 7:    4
8, 2, 8:    q+6
8, 2, 9:    3
8, 3, 1:    5*q^2+8*q+22
8, 3, 2:    2*q^2+12*q+43
8, 3, 3:    q^2+6*q+41
8, 3, 4:    2*q+20
8, 3, 5:    4*q+27
8, 3, 6:    2*q+28
8, 3, 7:    5
8, 3, 8:    6
8, 3, 9:    5
8, 4, 1:    6*q+9
8, 4, 2:    3*q+18
8, 4, 3:    2*q+20
8, 4, 4:    q+5
8, 4, 5:    12
8, 4, 6:    12
8, 4, 7:    3
8, 4, 8:    3
8, 4, 9:    1
8, 5, 1:    q^2+2*q+10
8, 5, 2:    2*q^2+6*q+24
8, 5, 3:    4*q+27
8, 5, 4:    12
8, 5, 5:    q^2+6*q+24
8, 5, 6:    2*q+26
8, 5, 7:    5
8, 5, 8:    2*q+12
8, 5, 9:    8
8, 5, 10:    3
8, 6, 1:    2*q+8
8, 6, 2:    4*q+24
8, 6, 3:    2*q+28
8, 6, 4:    12
8, 6, 5:    2*q+26
8, 6, 6:    q+28
8, 6, 7:    6
8, 6, 8:    12
8, 6, 9:    8
8, 6, 10:    2
8, 7, 1:    1
8, 7, 2:    4
8, 7, 3:    5
8, 7, 4:    3
8, 7, 5:    5
8, 7, 6:    6
8, 7, 7:    1
8, 7, 8:    2
8, 7, 9:    2
8, 8, 2:    q+6
8, 8, 3:    6
8, 8, 4:    3
8, 8, 5:    2*q+12
8, 8, 6:    12
8, 8, 7:    2
8, 8, 8:    q+10
8, 8, 9:    7
8, 8, 10:    4
8, 8, 11:    1
9, 1, 1:    3*q^3+4*q^2+8*q+13
9, 1, 2:    4*q^2+6*q+19
9, 1, 3:    5*q+19
9, 1, 4:    8
9, 1, 5:    q+6
9, 1, 6:    6
9, 1, 7:    1
9, 2, 1:    4*q^2+6*q+19
9, 2, 2:    q^2+8*q+34
9, 2, 3:    2*q+29
9, 2, 4:    14
9, 2, 5:    2*q+18
9, 2, 6:    16
9, 2, 7:    2
9, 2, 8:    3
9, 2, 9:    2
9, 3, 1:    5*q+19
9, 3, 2:    2*q+29
9, 3, 3:    q+30
9, 3, 4:    9
9, 3, 5:    18
9, 3, 6:    18
9, 3, 7:    4
9, 3, 8:    5
9, 3, 9:    2
9, 4, 1:    8
9, 4, 2:    14
9, 4, 3:    9
9, 4, 4:    9
9, 4, 5:    7
9, 4, 6:    8
9, 4, 7:    1
9, 4, 8:    1
9, 4, 9:    3
9, 5, 1:    q+6
9, 5, 2:    2*q+18
9, 5, 3:    18
9, 5, 4:    7
9, 5, 5:    q+19
9, 5, 6:    16
9, 5, 7:    2
9, 5, 8:    8
9, 5, 9:    4
9, 5, 10:    1
9, 6, 1:    6
9, 6, 2:    16
9, 6, 3:    18
9, 6, 4:    8
9, 6, 5:    16
9, 6, 6:    18
9, 6, 7:    4
9, 6, 8:    8
9, 6, 9:    6
9, 6, 10:    2
9, 7, 1:    1
9, 7, 2:    2
9, 7, 3:    4
9, 7, 4:    1
9, 7, 5:    2
9, 7, 6:    4
9, 7, 7:    2
9, 7, 8:    2
9, 7, 9:    1
9, 7, 10:    1
9, 8, 2:    3
9, 8, 3:    5
9, 8, 4:    1
9, 8, 5:    8
9, 8, 6:    8
9, 8, 7:    2
9, 8, 8:    7
9, 8, 9:    3
9, 8, 10:    2
9, 9, 2:    2
9, 9, 3:    2
9, 9, 4:    3
9, 9, 5:    4
9, 9, 6:    6
9, 9, 7:    1
9, 9, 8:    3
9, 9, 9:    4
9, 9, 10:    2
9, 9, 11:    1
10, 1, 1:    7
10, 1, 2:    5
10, 1, 3:    3
10, 1, 4:    1
10, 2, 1:    5
10, 2, 2:    8
10, 2, 3:    6
10, 2, 4:    2
10, 2, 5:    4
10, 2, 6:    2
10, 3, 1:    3
10, 3, 2:    6
10, 3, 3:    7
10, 3, 4:    3
10, 3, 5:    3
10, 3, 6:    4
10, 3, 7:    1
10, 4, 1:    1
10, 4, 2:    2
10, 4, 3:    3
10, 4, 4:    2
10, 4, 5:    1
10, 4, 6:    2
10, 5, 2:    4
10, 5, 3:    3
10, 5, 4:    1
10, 5, 5:    6
10, 5, 6:    4
10, 5, 8:    3
10, 5, 9:    1
10, 6, 2:    2
10, 6, 3:    4
10, 6, 4:    2
10, 6, 5:    4
10, 6, 6:    6
10, 6, 7:    2
10, 6, 8:    2
10, 6, 9:    2
10, 7, 3:    1
10, 7, 6:    2
10, 7, 7:    1
10, 7, 9:    1
10, 8, 5:    3
10, 8, 6:    2
10, 8, 8:    4
10, 8, 9:    2
10, 8, 10:    2
10, 9, 5:    1
10, 9, 6:    2
10, 9, 7:    1
10, 9, 8:    2
10, 9, 9:    2
10, 9, 10:    1
10, 10, 8:    2
10, 10, 9:    1
10, 10, 10:    2
10, 10, 11:    1
11, 1, 1:    1
11, 2, 2:    1
11, 3, 3:    1
11, 4, 4:    1
11, 5, 5:    1
11, 6, 6:    1
11, 7, 7:    1
11, 8, 8:    1
11, 9, 9:    1
11, 10, 10:    1
11, 11, 11:    1

(C) 2005 Frank Lübeck