Character of tensor product of linear representations is product of characters
From Groupprops
Statement
Statement for a field
Suppose is a group (not necessarily finite) and
are finite-dimensional linear representations of
over a field
. Denote by
respectively the characters of
and
. Denote by
the tensor product of linear representations
and
and by
its character. Then, for any
, we have:
In point-free notation, this states that .