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GL₆(q) for any q, or SL₆(q) for q = 2 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:    q^10+q^8+q^7+3*q^6+q^5+4*q^4+3*q^3+3*q^2+4*q+1
1, 1, 2:    q^9+q^8+2*q^7+4*q^6+5*q^5+6*q^4+11*q^3+9*q^2+12*q+5
1, 1, 3:    q^8+q^7+3*q^6+4*q^5+8*q^4+9*q^3+13*q^2+15*q+9
1, 1, 4:    q^7+2*q^5+3*q^4+4*q^3+6*q^2+8*q+5
1, 1, 5:    q^7+q^6+4*q^5+4*q^4+9*q^3+9*q^2+15*q+10
1, 1, 6:    q^6+2*q^5+4*q^4+7*q^3+12*q^2+16*q+16
1, 1, 7:    q^4+3*q^2+3*q+5
1, 1, 8:    q^4+2*q^3+4*q^2+6*q+10
1, 1, 9:    q^3+2*q^2+4*q+9
1, 1, 10:    5
1, 1, 11:    1
2, 1, 1:    q^9+q^8+2*q^7+4*q^6+5*q^5+6*q^4+11*q^3+9*q^2+12*q+5
2, 1, 2:    q^8+2*q^7+5*q^6+8*q^5+13*q^4+20*q^3+23*q^2+33*q+20
2, 1, 3:    q^7+2*q^6+6*q^5+10*q^4+19*q^3+25*q^2+39*q+30
2, 1, 4:    q^6+q^5+4*q^4+6*q^3+12*q^2+16*q+15
2, 1, 5:    q^6+3*q^5+6*q^4+12*q^3+19*q^2+28*q+30
2, 1, 6:    q^5+4*q^4+8*q^3+18*q^2+31*q+40
2, 1, 7:    q^3+2*q^2+6*q+10
2, 1, 8:    2*q^3+4*q^2+8*q+20
2, 1, 9:    2*q^2+4*q+15
2, 1, 10:    5
2, 2, 1:    q^8+2*q^7+5*q^6+8*q^5+13*q^4+20*q^3+23*q^2+33*q+20
2, 2, 2:    q^7+4*q^6+10*q^5+18*q^4+36*q^3+48*q^2+76*q+65
2, 2, 3:    q^6+4*q^5+12*q^4+26*q^3+46*q^2+81*q+87
2, 2, 4:    q^5+3*q^4+8*q^3+18*q^2+36*q+42
2, 2, 5:    2*q^5+6*q^4+16*q^3+30*q^2+56*q+76
2, 2, 6:    2*q^4+8*q^3+24*q^2+54*q+96
2, 2, 7:    2*q^2+8*q+23
2, 2, 8:    q^3+6*q^2+12*q+38
2, 2, 9:    q^2+6*q+30
2, 2, 10:    8
2, 2, 11:    1
3, 1, 1:    q^8+q^7+3*q^6+4*q^5+8*q^4+9*q^3+13*q^2+15*q+9
3, 1, 2:    q^7+2*q^6+6*q^5+10*q^4+19*q^3+25*q^2+39*q+30
3, 1, 3:    q^6+2*q^5+7*q^4+13*q^3+25*q^2+40*q+42
3, 1, 4:    q^5+q^4+5*q^3+9*q^2+18*q+21
3, 1, 5:    q^5+3*q^4+9*q^3+15*q^2+30*q+36
3, 1, 6:    q^4+4*q^3+12*q^2+27*q+48
3, 1, 7:    q^2+3*q+12
3, 1, 8:    3*q^2+6*q+18
3, 1, 9:    3*q+15
3, 1, 10:    3
3, 2, 1:    q^7+2*q^6+6*q^5+10*q^4+19*q^3+25*q^2+39*q+30
3, 2, 2:    q^6+4*q^5+12*q^4+26*q^3+46*q^2+81*q+87
3, 2, 3:    q^5+4*q^4+16*q^3+35*q^2+79*q+111
3, 2, 4:    q^4+3*q^3+12*q^2+30*q+51
3, 2, 5:    2*q^4+8*q^3+23*q^2+52*q+90
3, 2, 6:    2*q^3+12*q^2+42*q+108
3, 2, 7:    4*q+24
3, 2, 8:    2*q^2+10*q+39
3, 2, 9:    2*q+27
3, 2, 10:    6
3, 3, 1:    q^6+2*q^5+7*q^4+13*q^3+25*q^2+40*q+42
3, 3, 2:    q^5+4*q^4+16*q^3+35*q^2+79*q+111
3, 3, 3:    q^4+5*q^3+22*q^2+64*q+129
3, 3, 4:    q^3+5*q^2+24*q+60
3, 3, 5:    3*q^3+12*q^2+44*q+102
3, 3, 6:    4*q^2+28*q+114
3, 3, 7:    q+22
3, 3, 8:    q^2+6*q+39
3, 3, 9:    q+28
3, 3, 10:    7
3, 3, 11:    1
4, 1, 1:    q^7+2*q^5+3*q^4+4*q^3+6*q^2+8*q+5
4, 1, 2:    q^6+q^5+4*q^4+6*q^3+12*q^2+16*q+15
4, 1, 3:    q^5+q^4+5*q^3+9*q^2+18*q+21
4, 1, 4:    q^4+4*q^2+6*q+10
4, 1, 5:    q^4+2*q^3+6*q^2+13*q+16
4, 1, 6:    q^3+3*q^2+10*q+22
4, 1, 7:    q+6
4, 1, 8:    4*q+7
4, 1, 9:    6
4, 1, 10:    1
4, 2, 1:    q^6+q^5+4*q^4+6*q^3+12*q^2+16*q+15
4, 2, 2:    q^5+3*q^4+8*q^3+18*q^2+36*q+42
4, 2, 3:    q^4+3*q^3+12*q^2+30*q+51
4, 2, 4:    q^3+3*q^2+11*q+25
4, 2, 5:    2*q^3+6*q^2+22*q+41
4, 2, 6:    2*q^2+14*q+48
4, 2, 7:    9
4, 2, 8:    3*q+16
4, 2, 9:    12
4, 2, 10:    2
4, 3, 1:    q^5+q^4+5*q^3+9*q^2+18*q+21
4, 3, 2:    q^4+3*q^3+12*q^2+30*q+51
4, 3, 3:    q^3+5*q^2+24*q+60
4, 3, 4:    q^2+6*q+24
4, 3, 5:    3*q^2+15*q+45
4, 3, 6:    8*q+48
4, 3, 7:    10
4, 3, 8:    2*q+18
4, 3, 9:    9
4, 3, 10:    3
4, 4, 1:    q^4+4*q^2+6*q+10
4, 4, 2:    q^3+3*q^2+11*q+25
4, 4, 3:    q^2+6*q+24
4, 4, 4:    q^2+2*q+14
4, 4, 5:    6*q+19
4, 4, 6:    2*q+20
4, 4, 7:    3
4, 4, 8:    q+5
4, 4, 9:    7
4, 4, 10:    2
4, 4, 11:    1
5, 1, 1:    q^7+q^6+4*q^5+4*q^4+9*q^3+9*q^2+15*q+10
5, 1, 2:    q^6+3*q^5+6*q^4+12*q^3+19*q^2+28*q+30
5, 1, 3:    q^5+3*q^4+9*q^3+15*q^2+30*q+36
5, 1, 4:    q^4+2*q^3+6*q^2+13*q+16
5, 1, 5:    2*q^4+3*q^3+10*q^2+16*q+30
5, 1, 6:    2*q^3+6*q^2+16*q+32
5, 1, 7:    3*q+6
5, 1, 8:    q^2+2*q+10
5, 1, 9:    q+6
5, 2, 1:    q^6+3*q^5+6*q^4+12*q^3+19*q^2+28*q+30
5, 2, 2:    2*q^5+6*q^4+16*q^3+30*q^2+56*q+76
5, 2, 3:    2*q^4+8*q^3+23*q^2+52*q+90
5, 2, 4:    2*q^3+6*q^2+22*q+41
5, 2, 5:    q^4+5*q^3+14*q^2+33*q+66
5, 2, 6:    q^3+7*q^2+28*q+78
5, 2, 7:    2*q+17
5, 2, 8:    2*q^2+6*q+24
5, 2, 9:    2*q+18
5, 2, 10:    4
5, 3, 1:    q^5+3*q^4+9*q^3+15*q^2+30*q+36
5, 3, 2:    2*q^4+8*q^3+23*q^2+52*q+90
5, 3, 3:    3*q^3+12*q^2+44*q+102
5, 3, 4:    3*q^2+15*q+45
5, 3, 5:    q^3+8*q^2+27*q+78
5, 3, 6:    2*q^2+18*q+84
5, 3, 7:    q+16
5, 3, 8:    4*q+27
5, 3, 9:    18
5, 3, 10:    3
5, 4, 1:    q^4+2*q^3+6*q^2+13*q+16
5, 4, 2:    2*q^3+6*q^2+22*q+41
5, 4, 3:    3*q^2+15*q+45
5, 4, 4:    6*q+19
5, 4, 5:    q^2+9*q+36
5, 4, 6:    4*q+36
5, 4, 7:    7
5, 4, 8:    12
5, 4, 9:    7
5, 4, 10:    1
5, 5, 1:    2*q^4+3*q^3+10*q^2+16*q+30
5, 5, 2:    q^4+5*q^3+14*q^2+33*q+66
5, 5, 3:    q^3+8*q^2+27*q+78
5, 5, 4:    q^2+9*q+36
5, 5, 5:    2*q^3+6*q^2+24*q+55
5, 5, 6:    2*q^2+14*q+68
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:    q^6+2*q^5+4*q^4+7*q^3+12*q^2+16*q+16
6, 1, 2:    q^5+4*q^4+8*q^3+18*q^2+31*q+40
6, 1, 3:    q^4+4*q^3+12*q^2+27*q+48
6, 1, 4:    q^3+3*q^2+10*q+22
6, 1, 5:    2*q^3+6*q^2+16*q+32
6, 1, 6:    2*q^2+12*q+38
6, 1, 7:    8
6, 1, 8:    2*q+8
6, 1, 9:    6
6, 2, 1:    q^5+4*q^4+8*q^3+18*q^2+31*q+40
6, 2, 2:    2*q^4+8*q^3+24*q^2+54*q+96
6, 2, 3:    2*q^3+12*q^2+42*q+108
6, 2, 4:    2*q^2+14*q+48
6, 2, 5:    q^3+7*q^2+28*q+78
6, 2, 6:    q^2+15*q+84
6, 2, 7:    16
6, 2, 8:    4*q+24
6, 2, 9:    16
6, 2, 10:    2
6, 3, 1:    q^4+4*q^3+12*q^2+27*q+48
6, 3, 2:    2*q^3+12*q^2+42*q+108
6, 3, 3:    4*q^2+28*q+114
6, 3, 4:    8*q+48
6, 3, 5:    2*q^2+18*q+84
6, 3, 6:    8*q+86
6, 3, 7:    16
6, 3, 8:    2*q+28
6, 3, 9:    18
6, 3, 10:    4
6, 4, 1:    q^3+3*q^2+10*q+22
6, 4, 2:    2*q^2+14*q+48
6, 4, 3:    8*q+48
6, 4, 4:    2*q+20
6, 4, 5:    4*q+36
6, 4, 6:    2*q+36
6, 4, 7:    6
6, 4, 8:    12
6, 4, 9:    8
6, 4, 10:    2
6, 5, 1:    2*q^3+6*q^2+16*q+32
6, 5, 2:    q^3+7*q^2+28*q+78
6, 5, 3:    2*q^2+18*q+84
6, 5, 4:    4*q+36
6, 5, 5:    2*q^2+14*q+68
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:    2*q^2+12*q+38
6, 6, 2:    q^2+15*q+84
6, 6, 3:    8*q+86
6, 6, 4:    2*q+36
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:    q^4+3*q^2+3*q+5
7, 1, 2:    q^3+2*q^2+6*q+10
7, 1, 3:    q^2+3*q+12
7, 1, 4:    q+6
7, 1, 5:    3*q+6
7, 1, 6:    8
7, 1, 7:    2
7, 1, 8:    1
7, 1, 9:    1
7, 2, 1:    q^3+2*q^2+6*q+10
7, 2, 2:    2*q^2+8*q+23
7, 2, 3:    4*q+24
7, 2, 4:    9
7, 2, 5:    2*q+17
7, 2, 6:    16
7, 2, 7:    2
7, 2, 8:    4
7, 2, 9:    2
7, 3, 1:    q^2+3*q+12
7, 3, 2:    4*q+24
7, 3, 3:    q+22
7, 3, 4:    10
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:    q+6
7, 4, 2:    9
7, 4, 3:    10
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:    3*q+6
7, 5, 2:    2*q+17
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:    8
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:    q^4+2*q^3+4*q^2+6*q+10
8, 1, 2:    2*q^3+4*q^2+8*q+20
8, 1, 3:    3*q^2+6*q+18
8, 1, 4:    4*q+7
8, 1, 5:    q^2+2*q+10
8, 1, 6:    2*q+8
8, 1, 7:    1
8, 2, 1:    2*q^3+4*q^2+8*q+20
8, 2, 2:    q^3+6*q^2+12*q+38
8, 2, 3:    2*q^2+10*q+39
8, 2, 4:    3*q+16
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:    3*q^2+6*q+18
8, 3, 2:    2*q^2+10*q+39
8, 3, 3:    q^2+6*q+39
8, 3, 4:    2*q+18
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:    4*q+7
8, 4, 2:    3*q+16
8, 4, 3:    2*q+18
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:    q^3+2*q^2+4*q+9
9, 1, 2:    2*q^2+4*q+15
9, 1, 3:    3*q+15
9, 1, 4:    6
9, 1, 5:    q+6
9, 1, 6:    6
9, 1, 7:    1
9, 2, 1:    2*q^2+4*q+15
9, 2, 2:    q^2+6*q+30
9, 2, 3:    2*q+27
9, 2, 4:    12
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:    3*q+15
9, 3, 2:    2*q+27
9, 3, 3:    q+28
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:    6
9, 4, 2:    12
9, 4, 3:    9
9, 4, 4:    7
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:    5
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