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SL6(q) for q = 1 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:    6*q^10+6*q^8+6*q^7+13*q^6+6*q^5+19*q^4+9*q^3+13*q^2+10*q+2
1, 1, 2:    6*q^9+6*q^8+12*q^7+19*q^6+25*q^5+26*q^4+42*q^3+32*q^2+31*q+11
1, 1, 3:    6*q^8+6*q^7+18*q^6+19*q^5+38*q^4+35*q^3+49*q^2+40*q+21
1, 1, 4:    6*q^7+12*q^5+13*q^4+19*q^3+19*q^2+24*q+8
1, 1, 5:    6*q^7+6*q^6+19*q^5+19*q^4+34*q^3+30*q^2+43*q+19
1, 1, 6:    6*q^6+12*q^5+19*q^4+32*q^3+43*q^2+45*q+35
1, 1, 7:    6*q^4+13*q^2+9*q+11
1, 1, 8:    6*q^4+7*q^3+14*q^2+16*q+21
1, 1, 9:    6*q^3+7*q^2+14*q+17
1, 1, 10:    10
1, 1, 11:    1
2, 1, 1:    6*q^9+6*q^8+12*q^7+19*q^6+25*q^5+26*q^4+42*q^3+32*q^2+31*q+11
2, 1, 2:    6*q^8+12*q^7+25*q^6+38*q^5+58*q^4+71*q^3+80*q^2+86*q+41
2, 1, 3:    6*q^7+12*q^6+31*q^5+45*q^4+75*q^3+84*q^2+103*q+59
2, 1, 4:    6*q^6+6*q^5+19*q^4+26*q^3+43*q^2+40*q+32
2, 1, 5:    6*q^6+13*q^5+26*q^4+42*q^3+60*q^2+67*q+60
2, 1, 6:    6*q^5+19*q^4+33*q^3+59*q^2+81*q+74
2, 1, 7:    6*q^3+7*q^2+17*q+18
2, 1, 8:    7*q^3+9*q^2+18*q+33
2, 1, 9:    7*q^2+9*q+26
2, 1, 10:    5
2, 2, 1:    6*q^8+12*q^7+25*q^6+38*q^5+58*q^4+71*q^3+80*q^2+86*q+41
2, 2, 2:    6*q^7+19*q^6+45*q^5+73*q^4+122*q^3+148*q^2+179*q+124
2, 2, 3:    6*q^6+19*q^5+52*q^4+92*q^3+144*q^2+190*q+159
2, 2, 4:    6*q^5+13*q^4+33*q^3+56*q^2+88*q+71
2, 2, 5:    7*q^5+21*q^4+46*q^3+76*q^2+116*q+123
2, 2, 6:    7*q^4+28*q^3+65*q^2+115*q+155
2, 2, 7:    7*q^2+19*q+36
2, 2, 8:    q^3+11*q^2+17*q+49
2, 2, 9:    q^2+11*q+38
2, 2, 10:    8
2, 2, 11:    1
3, 1, 1:    6*q^8+6*q^7+18*q^6+19*q^5+38*q^4+35*q^3+49*q^2+40*q+21
3, 1, 2:    6*q^7+12*q^6+31*q^5+45*q^4+75*q^3+84*q^2+103*q+59
3, 1, 3:    6*q^6+12*q^5+37*q^4+54*q^3+92*q^2+105*q+86
3, 1, 4:    6*q^5+6*q^4+25*q^3+32*q^2+52*q+38
3, 1, 5:    6*q^5+13*q^4+34*q^3+46*q^2+74*q+64
3, 1, 6:    6*q^4+19*q^3+43*q^2+72*q+88
3, 1, 7:    6*q^2+9*q+24
3, 1, 8:    8*q^2+11*q+29
3, 1, 9:    8*q+23
3, 1, 10:    3
3, 2, 1:    6*q^7+12*q^6+31*q^5+45*q^4+75*q^3+84*q^2+103*q+59
3, 2, 2:    6*q^6+19*q^5+52*q^4+92*q^3+144*q^2+190*q+159
3, 2, 3:    6*q^5+19*q^4+62*q^3+110*q^2+189*q+190
3, 2, 4:    6*q^4+13*q^3+43*q^2+72*q+89
3, 2, 5:    7*q^4+23*q^3+59*q^2+102*q+141
3, 2, 6:    7*q^3+33*q^2+88*q+164
3, 2, 7:    10*q+34
3, 2, 8:    2*q^2+15*q+47
3, 2, 9:    2*q+33
3, 2, 10:    6
3, 3, 1:    6*q^6+12*q^5+37*q^4+54*q^3+92*q^2+105*q+86
3, 3, 2:    6*q^5+19*q^4+62*q^3+110*q^2+189*q+190
3, 3, 3:    6*q^4+21*q^3+75*q^2+150*q+218
3, 3, 4:    6*q^3+18*q^2+61*q+95
3, 3, 5:    8*q^3+28*q^2+84*q+146
3, 3, 6:    10*q^2+54*q+162
3, 3, 7:    2*q+31
3, 3, 8:    q^2+6*q+45
3, 3, 9:    q+31
3, 3, 10:    7
3, 3, 11:    1
4, 1, 1:    6*q^7+12*q^5+13*q^4+19*q^3+19*q^2+24*q+8
4, 1, 2:    6*q^6+6*q^5+19*q^4+26*q^3+43*q^2+40*q+32
4, 1, 3:    6*q^5+6*q^4+25*q^3+32*q^2+52*q+38
4, 1, 4:    6*q^4+19*q^2+17*q+22
4, 1, 5:    6*q^4+7*q^3+21*q^2+31*q+28
4, 1, 6:    6*q^3+13*q^2+28*q+41
4, 1, 7:    6*q+9
4, 1, 8:    9*q+9
4, 1, 9:    11
4, 1, 10:    1
4, 2, 1:    6*q^6+6*q^5+19*q^4+26*q^3+43*q^2+40*q+32
4, 2, 2:    6*q^5+13*q^4+33*q^3+56*q^2+88*q+71
4, 2, 3:    6*q^4+13*q^3+43*q^2+72*q+89
4, 2, 4:    6*q^3+10*q^2+29*q+41
4, 2, 5:    7*q^3+16*q^2+45*q+62
4, 2, 6:    7*q^2+32*q+71
4, 2, 7:    15
4, 2, 8:    3*q+21
4, 2, 9:    14
4, 2, 10:    2
4, 3, 1:    6*q^5+6*q^4+25*q^3+32*q^2+52*q+38
4, 3, 2:    6*q^4+13*q^3+43*q^2+72*q+89
4, 3, 3:    6*q^3+18*q^2+61*q+95
4, 3, 4:    6*q^2+14*q+42
4, 3, 5:    8*q^2+28*q+65
4, 3, 6:    16*q+66
4, 3, 7:    13
4, 3, 8:    2*q+20
4, 3, 9:    9
4, 3, 10:    3
4, 4, 1:    6*q^4+19*q^2+17*q+22
4, 4, 2:    6*q^3+10*q^2+29*q+41
4, 4, 3:    6*q^2+14*q+42
4, 4, 4:    3*q^2+7*q+21
4, 4, 5:    13*q+22
4, 4, 6:    4*q+28
4, 4, 7:    4
4, 4, 8:    q+5
4, 4, 9:    9
4, 4, 10:    2
4, 4, 11:    1
5, 1, 1:    6*q^7+6*q^6+19*q^5+19*q^4+34*q^3+30*q^2+43*q+19
5, 1, 2:    6*q^6+13*q^5+26*q^4+42*q^3+60*q^2+67*q+60
5, 1, 3:    6*q^5+13*q^4+34*q^3+46*q^2+74*q+64
5, 1, 4:    6*q^4+7*q^3+21*q^2+31*q+28
5, 1, 5:    7*q^4+8*q^3+25*q^2+32*q+49
5, 1, 6:    7*q^3+16*q^2+32*q+51
5, 1, 7:    8*q+7
5, 1, 8:    q^2+2*q+10
5, 1, 9:    q+6
5, 2, 1:    6*q^6+13*q^5+26*q^4+42*q^3+60*q^2+67*q+60
5, 2, 2:    7*q^5+21*q^4+46*q^3+76*q^2+116*q+123
5, 2, 3:    7*q^4+23*q^3+59*q^2+102*q+141
5, 2, 4:    7*q^3+16*q^2+45*q+62
5, 2, 5:    q^4+10*q^3+24*q^2+49*q+85
5, 2, 6:    q^3+12*q^2+44*q+99
5, 2, 7:    2*q+23
5, 2, 8:    2*q^2+6*q+24
5, 2, 9:    2*q+18
5, 2, 10:    4
5, 3, 1:    6*q^5+13*q^4+34*q^3+46*q^2+74*q+64
5, 3, 2:    7*q^4+23*q^3+59*q^2+102*q+141
5, 3, 3:    8*q^3+28*q^2+84*q+146
5, 3, 4:    8*q^2+28*q+65
5, 3, 5:    q^3+13*q^2+38*q+98
5, 3, 6:    2*q^2+24*q+100
5, 3, 7:    q+17
5, 3, 8:    4*q+27
5, 3, 9:    18
5, 3, 10:    3
5, 4, 1:    6*q^4+7*q^3+21*q^2+31*q+28
5, 4, 2:    7*q^3+16*q^2+45*q+62
5, 4, 3:    8*q^2+28*q+65
5, 4, 4:    13*q+22
5, 4, 5:    q^2+14*q+44
5, 4, 6:    4*q+44
5, 4, 7:    8
5, 4, 8:    12
5, 4, 9:    7
5, 4, 10:    1
5, 5, 1:    7*q^4+8*q^3+25*q^2+32*q+49
5, 5, 2:    q^4+10*q^3+24*q^2+49*q+85
5, 5, 3:    q^3+13*q^2+38*q+98
5, 5, 4:    q^2+14*q+44
5, 5, 5:    2*q^3+6*q^2+29*q+56
5, 5, 6:    2*q^2+14*q+74
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:    6*q^6+12*q^5+19*q^4+32*q^3+43*q^2+45*q+35
6, 1, 2:    6*q^5+19*q^4+33*q^3+59*q^2+81*q+74
6, 1, 3:    6*q^4+19*q^3+43*q^2+72*q+88
6, 1, 4:    6*q^3+13*q^2+28*q+41
6, 1, 5:    7*q^3+16*q^2+32*q+51
6, 1, 6:    7*q^2+28*q+59
6, 1, 7:    14
6, 1, 8:    2*q+8
6, 1, 9:    6
6, 2, 1:    6*q^5+19*q^4+33*q^3+59*q^2+81*q+74
6, 2, 2:    7*q^4+28*q^3+65*q^2+115*q+155
6, 2, 3:    7*q^3+33*q^2+88*q+164
6, 2, 4:    7*q^2+32*q+71
6, 2, 5:    q^3+12*q^2+44*q+99
6, 2, 6:    q^2+21*q+106
6, 2, 7:    18
6, 2, 8:    4*q+24
6, 2, 9:    16
6, 2, 10:    2
6, 3, 1:    6*q^4+19*q^3+43*q^2+72*q+88
6, 3, 2:    7*q^3+33*q^2+88*q+164
6, 3, 3:    10*q^2+54*q+162
6, 3, 4:    16*q+66
6, 3, 5:    2*q^2+24*q+100
6, 3, 6:    9*q+99
6, 3, 7:    18
6, 3, 8:    2*q+28
6, 3, 9:    18
6, 3, 10:    4
6, 4, 1:    6*q^3+13*q^2+28*q+41
6, 4, 2:    7*q^2+32*q+71
6, 4, 3:    16*q+66
6, 4, 4:    4*q+28
6, 4, 5:    4*q+44
6, 4, 6:    2*q+40
6, 4, 7:    6
6, 4, 8:    12
6, 4, 9:    8
6, 4, 10:    2
6, 5, 1:    7*q^3+16*q^2+32*q+51
6, 5, 2:    q^3+12*q^2+44*q+99
6, 5, 3:    2*q^2+24*q+100
6, 5, 4:    4*q+44
6, 5, 5:    2*q^2+14*q+74
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:    7*q^2+28*q+59
6, 6, 2:    q^2+21*q+106
6, 6, 3:    9*q+99
6, 6, 4:    2*q+40
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:    6*q^4+13*q^2+9*q+11
7, 1, 2:    6*q^3+7*q^2+17*q+18
7, 1, 3:    6*q^2+9*q+24
7, 1, 4:    6*q+9
7, 1, 5:    8*q+7
7, 1, 6:    14
7, 1, 7:    3
7, 1, 8:    1
7, 1, 9:    1
7, 2, 1:    6*q^3+7*q^2+17*q+18
7, 2, 2:    7*q^2+19*q+36
7, 2, 3:    10*q+34
7, 2, 4:    15
7, 2, 5:    2*q+23
7, 2, 6:    18
7, 2, 7:    2
7, 2, 8:    4
7, 2, 9:    2
7, 3, 1:    6*q^2+9*q+24
7, 3, 2:    10*q+34
7, 3, 3:    2*q+31
7, 3, 4:    13
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:    6*q+9
7, 4, 2:    15
7, 4, 3:    13
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:    8*q+7
7, 5, 2:    2*q+23
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:    14
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:    6*q^4+7*q^3+14*q^2+16*q+21
8, 1, 2:    7*q^3+9*q^2+18*q+33
8, 1, 3:    8*q^2+11*q+29
8, 1, 4:    9*q+9
8, 1, 5:    q^2+2*q+10
8, 1, 6:    2*q+8
8, 1, 7:    1
8, 2, 1:    7*q^3+9*q^2+18*q+33
8, 2, 2:    q^3+11*q^2+17*q+49
8, 2, 3:    2*q^2+15*q+47
8, 2, 4:    3*q+21
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:    8*q^2+11*q+29
8, 3, 2:    2*q^2+15*q+47
8, 3, 3:    q^2+6*q+45
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:    9*q+9
8, 4, 2:    3*q+21
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:    6*q^3+7*q^2+14*q+17
9, 1, 2:    7*q^2+9*q+26
9, 1, 3:    8*q+23
9, 1, 4:    11
9, 1, 5:    q+6
9, 1, 6:    6
9, 1, 7:    1
9, 2, 1:    7*q^2+9*q+26
9, 2, 2:    q^2+11*q+38
9, 2, 3:    2*q+33
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:    8*q+23
9, 3, 2:    2*q+33
9, 3, 3:    q+31
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:    11
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:    10
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