All Questions

This post is motivated by an exchange with Zhengwei Liu. It is more than the dual version of this post, because we consider any subgroup (instead of just maximal), and even more at the end... Let's ...

Let's first define what we mean by depth of a subgroup. Let $G$ be a finite group and $H$ a subgroup. Let $(V_i)_{i \in I}$ and $(W_j)_{j \in J}$ be the irreducible complex representations of $G$ ...