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Generic decomposition of tensor products

Here we provide some experimental data of multiplicities of unipotent (almost) characters in tensor products of unipotent (almost) characters in some series of finite groups of Lie type.

Some observations from these data are described in

Hiss,G. and Lübeck, F., Some observations on products of characters of finite classical groups, Proceedings of Finite Groups 2003, Gainesville (FL), in honor of J. G. Thompson's 70th birthday, de Gruyter (2004)

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The following series of groups were considered. In each case the multiplicities in question are described generically for all corresponding q as polynomials in q with integer coefficients (and often all coefficients are non-negative integers).

GL₂(q) for any q, or SL₂(q) for q = 0 mod 2
SL₂(q) for q = 1 mod 2
GL₃(q) for any q, or SL₃(q) for q = 0, 2 mod 3
SL₃(q) for q = 1 mod 3
GU₃(q) for any q, or SU₃(q) for q <> 2 mod 3
SU₃(q) for q = 2 mod 3
C_2,sc(q) or CSp₄(q) for q = 0 mod 2
C_2,sc(q) for q = 1 mod 2
CSp₄(q) for q = 1 mod 2
GL₄(q) for any q, or SL₄(q) for q = 0, 2 mod 4
SL₄(q) for q = 1 mod 4
SL₄(q) for q = 3 mod 4
GU₄(q) for any q, or SU₄(q) for q = 0 mod 2
SU₄(q) for q = 1 mod 4
SU₄(q) for q = 3 mod 4
B_3,sc(q) = C_3,sc(q) and CSp₆(q) for q = 0 mod 2
B_3,sc(q) for q = 1 mod 4
B_3,sc(q) for q = 3 mod 4
C_3,sc(q) for q = 1 mod 2
CSp₆(q) for q = 1 mod 2
GL₅(q) for any q, or SL₅(q) for q <> 1 mod 5
SL₅(q) for q = 1 mod 5
GU₅(q) for any q, or SU₅(q) for q <> 4 mod 5
SU₅(q) for q = 4 mod 5
B_4,sc(q) = C_4,sc(q) and CSp₈(q) for q = 0 mod 2
B_4,sc(q) for q = 1 mod 2
C_4,sc(q) for q = 1 mod 2
CSp₈(q) for q = 1 mod 2
D_4,sc(q) for q = 0 mod 2
D_4,sc(q) for q = 1 mod 2
³D₄(q) for q = 0 mod 2
³D₄(q) for q = 1 mod 2
GL₆(q) for any q, or SL₆(q) for q = 2 mod 6
SL₆(q) for q = 1 mod 6
SL₆(q) for q = 3, 5 mod 6
SL₆(q) for q = 4 mod 6
GU₆(q) for any q, or SU₆(q) for q = 4 mod 6
SU₆(q) for q = 1, 3 mod 6
SU₆(q) for q = 2 mod 6
SU₆(q) for q = 5 mod 6
GL₇(q) for any q, or SL₇(q) for q <> 1 mod 7
SL₇(q) for q = 1 mod 7
GU₇(q) for any q, or SU₇(q) for q <> 6 mod 7
SU₇(q) for q = 6 mod 7
E_6,sc(q) for q = 1 mod 6
GL₈(q) for any q, or SL₈(q) for q = 0 mod 2
SL₈(q) for q = 1 mod 8
SL₈(q) for q = 3, 7 mod 8
SL₈(q) for q = 5 mod 8
GU₈(q) for any q, or SU₈(q) for q = 0 mod 2
SU₈(q) for q = 1, 5 mod 8
SU₈(q) for q = 3 mod 8
SU₈(q) for q = 7 mod 8