# Questions tagged [representation-theory]

Representation theory studies (among other things) representations of groups by finite matrices. The non-commutative analog of classical Fourier transforms.

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### Application of Hilbert's basis theorem in representation theory

In Smalo: Degenerations of Representations of Associative Algebras, Milan J. Math., 2008 there is an application of Hilbert's basis theorem that I don't understand: Two orders are defined on the set ...
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### Tate conjecture for Fermat varieties

I've been looking at Tate's Algebraic Cycles and Poles of Zeta Functions (hard to find online... Google books outline here) and have a question about his work on (conjecturing!) the Tate conjecture ...
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### Subgroups as isotropy subgroups and regular orbits on tuples

Is there some natural or character-theoretic description of the minimum value of d such that G has a regular orbit on Ωd, where G is a finite group acting faithfully on a set Ω? Motivation: In some ...
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### If $g$ is commutator then so is $g^m$ for $(m,o(g))=1$

There are certain theorems in finite group theory whose proofs involve character theory and for which there are still no character-free proofs. Among such is Frobenius theorem on transitive ...
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### $\text{SL}(2, \mathbb{F}_q)$, for which characters is the $G$-representation irreducible?

Followup to here. Let $\mathbb{F}$ be a finite field with $q$ elements, and let $G = \text{SL}_2(\mathbb{F})$. The group $G$ acts linearly on the $2$-dimensional vector space $\mathbb{F}^2$ and fixes ...
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### Can this puzzle be solved using the representation theory of quivers?

This riddle originates in the youtube video here. It's mathematical content was summarised here as follows: There's a $5\times 5$ grid of nodes, all nodes are (bidirectionally) connected to their ...
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### Frobenius determinant theorem

Can anyone please recommend a paper or a book that gives a detailed proof of the Frobenius determinant theorem? I have read some few papers I saw online but their information are not sufficient for my ...