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For this question all groups are finite, and representations are over $\mathbb{C}$. The setup is that we have $N$ a normal subgroup of $G$, with abelian quotient $A$, and an irrep $V$ of $N$ that is i …

Let $G$ be a finite group, and $n$ an integer coprime to $|G|$. Then we have the following map, which is clearly not a morphism of groups in general: $$g\mapsto g^n.$$ This induces a linear automorphi …

Let $G$ be a finite group, and $R(G)$ its representation ring over $\mathbb{C}$. We have the Adams operations $\psi^k:R(G)\rightarrow R(G)$, given on the level of characters by: $$\chi_{\psi^k{V}}(g)= …

One interesting way to describe the ordinary (over $\mathbb{C}$) character theory of finite groups is to view the categories $Rep(G)$ together in a $2$ category with bimodules as morphisms. This $2$ c …

The setup is that we have a finite poset $P$, with a multiplicative rank function $r_{xy}:P\times P\rightarrow \mathbb{N}$, and a symmetric pairing $\langle\ ,\ \rangle:P\times P\rightarrow\mathbb{N}$ …

Tannaka duality for a finite group lets us recover the group algebra $\mathbb{C}[G]$ as the endomorphisms of the forgetful functor $F:RepG\rightarrow Vect$, and taking the monoidal automorphisms recov …

Given a ring $R$ with finite additive basis $\{e_i\}_{i=1}^{n}$, such that $e_i e_j=\sum c_{ijk}e_k$ with $c_{ijk}\in \mathbb{N}$, we define the Perron-Frobenius dimension $FPDim(e_i)$ of a basis elem …