So, since I’ll be talking about the symmetric group a bit, and since I still don’t have enough time for a deep post on it, I’ll take the opportunity to cover a quick and relevant lemma in group representation theory (referring as usual to the past blog post as background).

A **faithful representation** of a finite group is one where different elements of induce different linear transformations, i.e. is injective. The result is

Lemma 1If is a faithful representation of , then every simple representation of occurs as a direct summand in some tensor power .(more…)