Clifford theory relates the representation theory of a group to that of a normal subgroup. A good reference for this is Curtis and Reiner's "Methods in Representation theory II" T …

The question is in the title, a rephrasing could be is any finite group representable as the automorphism group of a finite tree, if not what is typically unrepresentable? In c …

Let say Z is a sum of n-roots of unity and thus an algebraic integer, and D is an rational integer. If |z+D| is an integer, what can we conclude regarding Z? can we say |Z| is in …

Suppose $G_1, \ldots, G_k$ are unitary, Hermitian, and anti-commuting, as well as $F_1, \ldots, F_k$. If they are similar, i.e., there exists $T \in GL_n(\mathbb{C})$ such that $$ …

This must be a naive question, but I'm wondering about the definition of the quasi-unipotent monodromy for general (not only 1-parameter families). The problem is that usually in t …

Let $G$ be a finite group and $N$ be a normal subgoup of G. Suppose that $\chi \in Irr(G)$. If $\theta , \lambda \in Irr(N)$, such that $[\chi_{N}, \theta]>0$ , $[\chi_{N}, \lamb …

I guess that finitely generated artin moudles are noeterian, but i haven't got a proof. I believe it is right, so could you show me how to prove it?

Is there any description of indecomposable modules and irreducible morphisms over self-injective algebras of finite representaion type. I am intrested mainly in such description fo …

Let $G$ be a Lie group and $\pi$ a continuous action on $V$ a Fréchet space. This action induces a representation of the compact-supported function $C_c(G)$ (with convolution as p …

I am asking about good references (both books and papers) for the well-known Borel-Weil theorem! Thank you very much!

In axioms for VOA, we know that any two vertex operators satisfy commutativity and associativity. But for two intertwining operators, commutativity and associativity are not alway …

What does "The associated linear representation of a group or a semigroup" or "The representation associated to a module" mean?

Consider $\Lambda^p(C^n\otimes C^n)=\oplus_{\pi}S_{\pi}C^n\otimes S_{\pi'}C^n$ as a $GL_n\times GL_n$-module. This space has dimension $\binom {n^2}p$. I would like any information …