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SL6(q) for q = 3, 5 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:    2*q^10+2*q^8+2*q^7+5*q^6+2*q^5+7*q^4+5*q^3+5*q^2+6*q+2
1, 1, 2:    2*q^9+2*q^8+4*q^7+7*q^6+9*q^5+10*q^4+18*q^3+14*q^2+17*q+7
1, 1, 3:    2*q^8+2*q^7+6*q^6+7*q^5+14*q^4+15*q^3+21*q^2+22*q+13
1, 1, 4:    2*q^7+4*q^5+5*q^4+7*q^3+9*q^2+12*q+6
1, 1, 5:    2*q^7+2*q^6+7*q^5+7*q^4+14*q^3+14*q^2+21*q+13
1, 1, 6:    2*q^6+4*q^5+7*q^4+12*q^3+19*q^2+23*q+21
1, 1, 7:    2*q^4+5*q^2+5*q+7
1, 1, 8:    2*q^4+3*q^3+6*q^2+8*q+13
1, 1, 9:    2*q^3+3*q^2+6*q+11
1, 1, 10:    6
1, 1, 11:    1
2, 1, 1:    2*q^9+2*q^8+4*q^7+7*q^6+9*q^5+10*q^4+18*q^3+14*q^2+17*q+7
2, 1, 2:    2*q^8+4*q^7+9*q^6+14*q^5+22*q^4+31*q^3+36*q^2+46*q+27
2, 1, 3:    2*q^7+4*q^6+11*q^5+17*q^4+31*q^3+38*q^2+55*q+39
2, 1, 4:    2*q^6+2*q^5+7*q^4+10*q^3+19*q^2+22*q+20
2, 1, 5:    2*q^6+5*q^5+10*q^4+18*q^3+28*q^2+37*q+38
2, 1, 6:    2*q^5+7*q^4+13*q^3+27*q^2+43*q+50
2, 1, 7:    2*q^3+3*q^2+9*q+12
2, 1, 8:    3*q^3+5*q^2+10*q+23
2, 1, 9:    3*q^2+5*q+18
2, 1, 10:    5
2, 2, 1:    2*q^8+4*q^7+9*q^6+14*q^5+22*q^4+31*q^3+36*q^2+46*q+27
2, 2, 2:    2*q^7+7*q^6+17*q^5+29*q^4+54*q^3+70*q^2+101*q+82
2, 2, 3:    2*q^6+7*q^5+20*q^4+40*q^3+68*q^2+108*q+109
2, 2, 4:    2*q^5+5*q^4+13*q^3+26*q^2+48*q+51
2, 2, 5:    3*q^5+9*q^4+22*q^3+40*q^2+70*q+89
2, 2, 6:    3*q^4+12*q^3+33*q^2+69*q+113
2, 2, 7:    3*q^2+11*q+28
2, 2, 8:    q^3+7*q^2+13*q+41
2, 2, 9:    q^2+7*q+32
2, 2, 10:    8
2, 2, 11:    1
3, 1, 1:    2*q^8+2*q^7+6*q^6+7*q^5+14*q^4+15*q^3+21*q^2+22*q+13
3, 1, 2:    2*q^7+4*q^6+11*q^5+17*q^4+31*q^3+38*q^2+55*q+39
3, 1, 3:    2*q^6+4*q^5+13*q^4+22*q^3+40*q^2+57*q+56
3, 1, 4:    2*q^5+2*q^4+9*q^3+14*q^2+26*q+26
3, 1, 5:    2*q^5+5*q^4+14*q^3+22*q^2+40*q+44
3, 1, 6:    2*q^4+7*q^3+19*q^2+38*q+60
3, 1, 7:    2*q^2+5*q+16
3, 1, 8:    4*q^2+7*q+21
3, 1, 9:    4*q+17
3, 1, 10:    3
3, 2, 1:    2*q^7+4*q^6+11*q^5+17*q^4+31*q^3+38*q^2+55*q+39
3, 2, 2:    2*q^6+7*q^5+20*q^4+40*q^3+68*q^2+108*q+109
3, 2, 3:    2*q^5+7*q^4+26*q^3+52*q^2+107*q+136
3, 2, 4:    2*q^4+5*q^3+19*q^2+40*q+63
3, 2, 5:    3*q^4+11*q^3+31*q^2+64*q+105
3, 2, 6:    3*q^3+17*q^2+54*q+126
3, 2, 7:    6*q+28
3, 2, 8:    2*q^2+11*q+41
3, 2, 9:    2*q+29
3, 2, 10:    6
3, 3, 1:    2*q^6+4*q^5+13*q^4+22*q^3+40*q^2+57*q+56
3, 3, 2:    2*q^5+7*q^4+26*q^3+52*q^2+107*q+136
3, 3, 3:    2*q^4+9*q^3+35*q^2+88*q+160
3, 3, 4:    2*q^3+8*q^2+33*q+71
3, 3, 5:    4*q^3+16*q^2+54*q+116
3, 3, 6:    6*q^2+36*q+132
3, 3, 7:    2*q+27
3, 3, 8:    q^2+6*q+41
3, 3, 9:    q+29
3, 3, 10:    7
3, 3, 11:    1
4, 1, 1:    2*q^7+4*q^5+5*q^4+7*q^3+9*q^2+12*q+6
4, 1, 2:    2*q^6+2*q^5+7*q^4+10*q^3+19*q^2+22*q+20
4, 1, 3:    2*q^5+2*q^4+9*q^3+14*q^2+26*q+26
4, 1, 4:    2*q^4+7*q^2+9*q+14
4, 1, 5:    2*q^4+3*q^3+9*q^2+17*q+20
4, 1, 6:    2*q^3+5*q^2+14*q+27
4, 1, 7:    2*q+7
4, 1, 8:    5*q+7
4, 1, 9:    7
4, 1, 10:    1
4, 2, 1:    2*q^6+2*q^5+7*q^4+10*q^3+19*q^2+22*q+20
4, 2, 2:    2*q^5+5*q^4+13*q^3+26*q^2+48*q+51
4, 2, 3:    2*q^4+5*q^3+19*q^2+40*q+63
4, 2, 4:    2*q^3+4*q^2+15*q+29
4, 2, 5:    3*q^3+8*q^2+27*q+46
4, 2, 6:    3*q^2+18*q+55
4, 2, 7:    11
4, 2, 8:    3*q+17
4, 2, 9:    12
4, 2, 10:    2
4, 3, 1:    2*q^5+2*q^4+9*q^3+14*q^2+26*q+26
4, 3, 2:    2*q^4+5*q^3+19*q^2+40*q+63
4, 3, 3:    2*q^3+8*q^2+33*q+71
4, 3, 4:    2*q^2+8*q+30
4, 3, 5:    4*q^2+18*q+51
4, 3, 6:    10*q+54
4, 3, 7:    11
4, 3, 8:    2*q+18
4, 3, 9:    9
4, 3, 10:    3
4, 4, 1:    2*q^4+7*q^2+9*q+14
4, 4, 2:    2*q^3+4*q^2+15*q+29
4, 4, 3:    2*q^2+8*q+30
4, 4, 4:    q^2+3*q+15
4, 4, 5:    7*q+20
4, 4, 6:    2*q+22
4, 4, 7:    4
4, 4, 8:    q+5
4, 4, 9:    7
4, 4, 10:    2
4, 4, 11:    1
5, 1, 1:    2*q^7+2*q^6+7*q^5+7*q^4+14*q^3+14*q^2+21*q+13
5, 1, 2:    2*q^6+5*q^5+10*q^4+18*q^3+28*q^2+37*q+38
5, 1, 3:    2*q^5+5*q^4+14*q^3+22*q^2+40*q+44
5, 1, 4:    2*q^4+3*q^3+9*q^2+17*q+20
5, 1, 5:    3*q^4+4*q^3+13*q^2+20*q+35
5, 1, 6:    3*q^3+8*q^2+20*q+37
5, 1, 7:    4*q+7
5, 1, 8:    q^2+2*q+10
5, 1, 9:    q+6
5, 2, 1:    2*q^6+5*q^5+10*q^4+18*q^3+28*q^2+37*q+38
5, 2, 2:    3*q^5+9*q^4+22*q^3+40*q^2+70*q+89
5, 2, 3:    3*q^4+11*q^3+31*q^2+64*q+105
5, 2, 4:    3*q^3+8*q^2+27*q+46
5, 2, 5:    q^4+6*q^3+16*q^2+37*q+71
5, 2, 6:    q^3+8*q^2+32*q+85
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:    2*q^5+5*q^4+14*q^3+22*q^2+40*q+44
5, 3, 2:    3*q^4+11*q^3+31*q^2+64*q+105
5, 3, 3:    4*q^3+16*q^2+54*q+116
5, 3, 4:    4*q^2+18*q+51
5, 3, 5:    q^3+9*q^2+30*q+84
5, 3, 6:    2*q^2+20*q+90
5, 3, 7:    q+17
5, 3, 8:    4*q+27
5, 3, 9:    18
5, 3, 10:    3
5, 4, 1:    2*q^4+3*q^3+9*q^2+17*q+20
5, 4, 2:    3*q^3+8*q^2+27*q+46
5, 4, 3:    4*q^2+18*q+51
5, 4, 4:    7*q+20
5, 4, 5:    q^2+10*q+38
5, 4, 6:    4*q+38
5, 4, 7:    8
5, 4, 8:    12
5, 4, 9:    7
5, 4, 10:    1
5, 5, 1:    3*q^4+4*q^3+13*q^2+20*q+35
5, 5, 2:    q^4+6*q^3+16*q^2+37*q+71
5, 5, 3:    q^3+9*q^2+30*q+84
5, 5, 4:    q^2+10*q+38
5, 5, 5:    2*q^3+6*q^2+25*q+56
5, 5, 6:    2*q^2+14*q+70
5, 5, 7:    17
5, 5, 8:    q^2+6*q+24
5, 5, 9:    q+19
5, 5, 10:    6
5, 5, 11:    1
6, 1, 1:    2*q^6+4*q^5+7*q^4+12*q^3+19*q^2+23*q+21
6, 1, 2:    2*q^5+7*q^4+13*q^3+27*q^2+43*q+50
6, 1, 3:    2*q^4+7*q^3+19*q^2+38*q+60
6, 1, 4:    2*q^3+5*q^2+14*q+27
6, 1, 5:    3*q^3+8*q^2+20*q+37
6, 1, 6:    3*q^2+16*q+45
6, 1, 7:    10
6, 1, 8:    2*q+8
6, 1, 9:    6
6, 2, 1:    2*q^5+7*q^4+13*q^3+27*q^2+43*q+50
6, 2, 2:    3*q^4+12*q^3+33*q^2+69*q+113
6, 2, 3:    3*q^3+17*q^2+54*q+126
6, 2, 4:    3*q^2+18*q+55
6, 2, 5:    q^3+8*q^2+32*q+85
6, 2, 6:    q^2+17*q+92
6, 2, 7:    18
6, 2, 8:    4*q+24
6, 2, 9:    16
6, 2, 10:    2
6, 3, 1:    2*q^4+7*q^3+19*q^2+38*q+60
6, 3, 2:    3*q^3+17*q^2+54*q+126
6, 3, 3:    6*q^2+36*q+132
6, 3, 4:    10*q+54
6, 3, 5:    2*q^2+20*q+90
6, 3, 6:    9*q+93
6, 3, 7:    18
6, 3, 8:    2*q+28
6, 3, 9:    18
6, 3, 10:    4
6, 4, 1:    2*q^3+5*q^2+14*q+27
6, 4, 2:    3*q^2+18*q+55
6, 4, 3:    10*q+54
6, 4, 4:    2*q+22
6, 4, 5:    4*q+38
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:    3*q^3+8*q^2+20*q+37
6, 5, 2:    q^3+8*q^2+32*q+85
6, 5, 3:    2*q^2+20*q+90
6, 5, 4:    4*q+38
6, 5, 5:    2*q^2+14*q+70
6, 5, 6:    6*q+72
6, 5, 7:    12
6, 5, 8:    2*q+26
6, 5, 9:    16
6, 5, 10:    4
6, 6, 1:    3*q^2+16*q+45
6, 6, 2:    q^2+17*q+92
6, 6, 3:    9*q+93
6, 6, 4:    2*q+38
6, 6, 5:    6*q+72
6, 6, 6:    2*q+72
6, 6, 7:    15
6, 6, 8:    q+28
6, 6, 9:    18
6, 6, 10:    6
6, 6, 11:    1
7, 1, 1:    2*q^4+5*q^2+5*q+7
7, 1, 2:    2*q^3+3*q^2+9*q+12
7, 1, 3:    2*q^2+5*q+16
7, 1, 4:    2*q+7
7, 1, 5:    4*q+7
7, 1, 6:    10
7, 1, 7:    3
7, 1, 8:    1
7, 1, 9:    1
7, 2, 1:    2*q^3+3*q^2+9*q+12
7, 2, 2:    3*q^2+11*q+28
7, 2, 3:    6*q+28
7, 2, 4:    11
7, 2, 5:    2*q+19
7, 2, 6:    18
7, 2, 7:    2
7, 2, 8:    4
7, 2, 9:    2
7, 3, 1:    2*q^2+5*q+16
7, 3, 2:    6*q+28
7, 3, 3:    2*q+27
7, 3, 4:    11
7, 3, 5:    q+17
7, 3, 6:    18
7, 3, 7:    4
7, 3, 8:    5
7, 3, 9:    4
7, 3, 10:    1
7, 4, 1:    2*q+7
7, 4, 2:    11
7, 4, 3:    11
7, 4, 4:    4
7, 4, 5:    8
7, 4, 6:    6
7, 4, 7:    2
7, 4, 8:    3
7, 4, 9:    1
7, 5, 1:    4*q+7
7, 5, 2:    2*q+19
7, 5, 3:    q+17
7, 5, 4:    8
7, 5, 5:    17
7, 5, 6:    12
7, 5, 7:    2
7, 5, 8:    5
7, 5, 9:    2
7, 6, 1:    10
7, 6, 2:    18
7, 6, 3:    18
7, 6, 4:    6
7, 6, 5:    12
7, 6, 6:    15
7, 6, 7:    2
7, 6, 8:    6
7, 6, 9:    4
7, 6, 10:    2
7, 7, 1:    3
7, 7, 2:    2
7, 7, 3:    4
7, 7, 4:    2
7, 7, 5:    2
7, 7, 6:    2
7, 7, 7:    3
7, 7, 8:    1
7, 7, 9:    2
7, 7, 10:    1
7, 7, 11:    1
8, 1, 1:    2*q^4+3*q^3+6*q^2+8*q+13
8, 1, 2:    3*q^3+5*q^2+10*q+23
8, 1, 3:    4*q^2+7*q+21
8, 1, 4:    5*q+7
8, 1, 5:    q^2+2*q+10
8, 1, 6:    2*q+8
8, 1, 7:    1
8, 2, 1:    3*q^3+5*q^2+10*q+23
8, 2, 2:    q^3+7*q^2+13*q+41
8, 2, 3:    2*q^2+11*q+41
8, 2, 4:    3*q+17
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:    4*q^2+7*q+21
8, 3, 2:    2*q^2+11*q+41
8, 3, 3:    q^2+6*q+41
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:    5*q+7
8, 4, 2:    3*q+17
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:    2*q^3+3*q^2+6*q+11
9, 1, 2:    3*q^2+5*q+18
9, 1, 3:    4*q+17
9, 1, 4:    7
9, 1, 5:    q+6
9, 1, 6:    6
9, 1, 7:    1
9, 2, 1:    3*q^2+5*q+18
9, 2, 2:    q^2+7*q+32
9, 2, 3:    2*q+29
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:    4*q+17
9, 3, 2:    2*q+29
9, 3, 3:    q+29
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:    7
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:    6
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