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GL₅(q) for any q, or SL₅(q) for q <> 1 mod 5

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

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^6+q^4+2*q^3+q^2+3*q+1
1, 1, 2:    q^5+q^4+3*q^3+3*q^2+6*q+4
1, 1, 3:    q^4+q^3+3*q^2+5*q+5
1, 1, 4:    q^3+2*q^2+4*q+6
1, 1, 5:    q^2+2*q+5
1, 1, 6:    4
1, 1, 7:    1
2, 1, 1:    q^5+q^4+3*q^3+3*q^2+6*q+4
2, 1, 2:    q^4+3*q^3+5*q^2+11*q+12
2, 1, 3:    q^3+3*q^2+8*q+12
2, 1, 4:    2*q^2+4*q+12
2, 1, 5:    2*q+8
2, 1, 6:    4
2, 2, 1:    q^4+3*q^3+5*q^2+11*q+12
2, 2, 2:    2*q^3+6*q^2+16*q+28
2, 2, 3:    2*q^2+10*q+26
2, 2, 4:    q^2+6*q+21
2, 2, 5:    q+15
2, 2, 6:    6
2, 2, 7:    1
3, 1, 1:    q^4+q^3+3*q^2+5*q+5
3, 1, 2:    q^3+3*q^2+8*q+12
3, 1, 3:    q^2+4*q+12
3, 1, 4:    3*q+9
3, 1, 5:    7
3, 1, 6:    2
3, 2, 1:    q^3+3*q^2+8*q+12
3, 2, 2:    2*q^2+10*q+26
3, 2, 3:    4*q+22
3, 2, 4:    2*q+18
3, 2, 5:    10
3, 2, 6:    4
3, 3, 1:    q^2+4*q+12
3, 3, 2:    4*q+22
3, 3, 3:    q+17
3, 3, 4:    q+13
3, 3, 5:    8
3, 3, 6:    4
3, 3, 7:    1
4, 1, 1:    q^3+2*q^2+4*q+6
4, 1, 2:    2*q^2+4*q+12
4, 1, 3:    3*q+9
4, 1, 4:    q+6
4, 1, 5:    3
4, 2, 1:    2*q^2+4*q+12
4, 2, 2:    q^2+6*q+21
4, 2, 3:    2*q+18
4, 2, 4:    2*q+12
4, 2, 5:    8
4, 2, 6:    3
4, 3, 1:    3*q+9
4, 3, 2:    2*q+18
4, 3, 3:    q+13
4, 3, 4:    11
4, 3, 5:    6
4, 3, 6:    2
4, 4, 1:    q+6
4, 4, 2:    2*q+12
4, 4, 3:    11
4, 4, 4:    q+10
4, 4, 5:    7
4, 4, 6:    4
4, 4, 7:    1
5, 1, 1:    q^2+2*q+5
5, 1, 2:    2*q+8
5, 1, 3:    7
5, 1, 4:    3
5, 1, 5:    2
5, 2, 1:    2*q+8
5, 2, 2:    q+15
5, 2, 3:    10
5, 2, 4:    8
5, 2, 5:    4
5, 2, 6:    1
5, 3, 1:    7
5, 3, 2:    10
5, 3, 3:    8
5, 3, 4:    6
5, 3, 5:    4
5, 3, 6:    2
5, 4, 1:    3
5, 4, 2:    8
5, 4, 3:    6
5, 4, 4:    7
5, 4, 5:    3
5, 4, 6:    2
5, 5, 1:    2
5, 5, 2:    4
5, 5, 3:    4
5, 5, 4:    3
5, 5, 5:    3
5, 5, 6:    2
5, 5, 7:    1
6, 1, 1:    4
6, 1, 2:    4
6, 1, 3:    2
6, 2, 1:    4
6, 2, 2:    6
6, 2, 3:    4
6, 2, 4:    3
6, 2, 5:    1
6, 3, 1:    2
6, 3, 2:    4
6, 3, 3:    4
6, 3, 4:    2
6, 3, 5:    2
6, 4, 2:    3
6, 4, 3:    2
6, 4, 4:    4
6, 4, 5:    2
6, 4, 6:    2
6, 5, 2:    1
6, 5, 3:    2
6, 5, 4:    2
6, 5, 5:    2
6, 5, 6:    1
6, 6, 4:    2
6, 6, 5:    1
6, 6, 6:    2
6, 6, 7:    1
7, 1, 1:    1
7, 2, 2:    1
7, 3, 3:    1
7, 4, 4:    1
7, 5, 5:    1
7, 6, 6:    1
7, 7, 7:    1

(C) 2005 Frank Lübeck