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Let $[H,G]$ be an interval of finite groups. Definition: Let $W$ be a representation of $G$, and $X$ a subspace of $W$. Let the fixed-point subspace $W^{H}:=\{w \in W \ \vert \ kw=w \ , \forall h \...

An action of a group $G$ on a set $X \neq \emptyset$ is called transitive if $\forall x,y \in X$, $\exists g \in G$ such that $g.x = y$. It is called primitive if it is transitive and preserves no non-...

Let $G$ be a finite group. It admits finitely many irreducible complex representations $H_1, \dots, H_r$ which generate, for $\oplus$ and $\otimes$, the Grothendieck ring $\mathcal{G}(G)$ of $G$ (also ...

Let $G$ be a finite group and $k$ be a finite field (big enough) whith char$(k)=p$ and $p\mid |G|$. Let $M$ be a finitely generated $kG$-module. We denote the first syzygy of $M$ by $\Omega(M)$, i.e....

I asked the same question in MSE, but I didn't get any answer. So I decided to post it here, too. In Langlands' program, Satake correspondence gives a correspondence between unramified ...