# Tagged Questions

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### Definition of a splitting field of a finite group

This is a basic question from the journal 'Mathematische Zeitschrift' 208 (1991) page 243. Let $K/F$ be a finite Galois extension of number fields and $G={\rm Gal}(K/F)$. Also let $L$ be any number ...
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### Exterior square of multiset in representation theory

General Setting: In a paper I'm working on, the author uses multisets to describe the representation theory of the cyclic group $G = C_n = <\sigma>$ of ...
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### Homomorphisms from the additive groups of virtual characters into certain idele groups

This is a question from Frohlich's book 'Galois Module Structure of Algebraic Integers', Ch.1. Let $K$ be a number field and $\Omega_K=\text{Gal}(K^c/K)$ where $K^c$ is the separable closure of $K$. ...
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### Computing Brauer characters of a finite group

I am studying character theory from the book "Character Theory of Finite Groups" by Martin Isaac. (I am not too familiar with valuations and algebraic number theory.) In the last chapter on modular ...
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### Values of virtual characters

Let $G$ be a finite group. Let $K$ be a number field and $K^c\subset\mathbb{C}$ its algebraic (separable) closure. Denote by $R_G$ the additive group of functions generated by the characters of ...
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### bests book of representation theory for algebraic number theorists

I am looking for some of the best books on representation theory for an algebraic number theorists> I would prefer a book that is more number theoretical (e.g, galois representations, p adic ...
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### Introduction to the trace formula for people outside number theory

I am looking for references on the trace formula, by which I mean the Selberg trace formula and its successor the Arthur-Selberg trace formula. I am aware that there are "standard references" on the ...
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### Galois representations and normal bases

I am not very familiar with the theory of Galois representations, but I do know a bit about both Galois theory and representation theory. Recently I learned about the notion of a normal basis for a ...
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### Reduced norms of matrix algebras

I'm trying to understand a few basic notions on the reduced norm of division algebras, and more specifically the relation between the norm of an algebra and the norm of algebras similar to it. ...
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### How can I determine in practice whether two elliptic curves over $\mathbb{Q}$ have isomorphic $p$-torsion?

Let $E_1$ and $E_2$ be elliptic curves over $\mathbb{Q}$ with good, ordinary reduction at an odd prime $p$. I'm wondering how to determine whether $E_1[p]$ and $E_2[p]$ are isomorphic ...
### 2-Brauer characters of the symmetric group $\mathfrak{S}_3$
In a previous question, I asked how to compute Brauer characters of the alternating group $\mathfrak{A}_3$; the answer to this question provided a solution for all cyclic groups. I would now like to ...