Jan 27

We proved:
Irreps of GxH are each the tensor product of an irrep of G with one of H.
C[G] is the sum over irreps V of V^* @ V, as a GxG-representation.
Character tables are square, i.e. the number of irreps is the number of conjugacy classes.
If G > H, two finite groups, then H misses some conjugacy class of G.
If G = U(n), H = T^n, then H hits every conjugacy class of G.

We didn't prove, but it's true:
As an algebra, C[G] is the direct sum of matrix algebras End(V), V running over irreps.