[GAP Forum] tensor product of representations

[Victor D. Mazurov]

Dear forum,

How can I get a homomorphism from given representation of finite group to
the another one?

Example: By Atlas of FGR,
Matrices
​

[[0,1,0,0],
[1,1,0,0],
[0,0,0,1],
[0,0,1,1]
]*Z(2)
,
[[0,0,1,0],
[0,1,1,0],
[0,1,1,1],
[1,1,1,0]
]*Z(2)

generate​ a 4-dimensional representation U of alternating group A_8 over a
field of order 2 and
matrices

[[0,1,0,0,0,0],
[1,1,0,0,0,0],
[1,1,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]
]*Z(2)
,
[[1,1,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1],
[1,0,1,0,1,0]
]*Z(2)

​generate a 6-dimensional  representation V of A_8 over a field of order
2​.

How can I calculate H=Hom(U\otimes U,V) and, if H\ne 0, a homomorphism of
U\otimes U onto V?

Best wishes, Victor Mazurov

-- 
Victor Danilovich Mazurov
Institute of Mathematics
Novosibirsk 630090
Russia