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$\DeclareMathOperator\Comm{Comm}\DeclareMathOperator\Id{Id}$Consider the variety $\Comm$ of commuting matrices $[A,B]=0$ over some field $K$. It is much studied, and interesting for various reasons. ...

Let $V$ and $W$ be complex irreducible representations of $GL_n(F_q)$ where $F_q$ is finite field. Is the decomposition of $V \otimes W$ into irreducible representations known? PS Same question: ...

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 ...

Denote the symmetric group of order $n!$ by $S_n$. Let $H:=S_p$ for an odd prime $p$. Every finite field $k$ is a splitting field $(^*)$ for $kH$, in particular $k:=\mathbb{F}_p$. Questions: Is $k:=\...

Denote by $\mathbb{F}_q$ the finite field with $q$ elements, and $\operatorname{SL}_n(\mathbb{F}_q)$ the special linear group in $n$ variables. What is the minimum dimension of nontrivial real ...