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1answer
190 views

Representation quaternions as matrices

char F≠2, a,b invertable from F, A(a,b) - generalised quaternions. Using Artin–Wedderburn theorem there is a representation of them over F. I found representation as Q8 but it's not over F. So, how to ...
3
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1answer
238 views

Which finite group is not the automorphism group of some rooted finite trees

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 case of ambiguity : ...
2
votes
1answer
228 views

Reference for Clifford theory (of algebras)

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" Theorem 11.1. ...
3
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0answers
71 views

Description of modules over self-injective algebras of finite representation type

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 for nonstandard ...
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2answers
379 views

Similarity about unitary matrices

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 $$ G_i = T^{-1} F_i T ...
0
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1answer
387 views

When does the modulus of a sum of an integer and an algebraic integer equal an integer?

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 integer? Another ...
1
vote
1answer
144 views

irreducible constituent in Normal subgroup

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 $[\chi_{N}, \theta]>0$ , $[\chi_{N}, \lambda]>0$, is it ...
3
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1answer
409 views

Quasi-unipotent monodromy for general families

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 the books of ...
2
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0answers
180 views

distribution on Lie Groups and representations

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 product) by $f\in ...
3
votes
2answers
399 views

Borel-Weil Theorem-References

I am asking about good references (both books and papers) for the well-known Borel-Weil theorem! Thank you very much!
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0answers
201 views

distribution of Young diagrams

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 on the shapes of ...