Matrix representation

Convolution of matrix representations

Let be the entries of concrete realizations of unitary irreps. Then the group ring convolution is given by1 #m/thm/rep

Proof

Using orthogonality of irreps and the fact that

as required.

#state/tidy | #lang/en | #SemBr

Footnotes

  1. 1996, Representations of finite and compact groups, §III.1, p. 38 ↩