The representation tag has no wiki summary.

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### 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 ...

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258 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 :
...

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### 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.
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### 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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395 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
...

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### 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 ...

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### 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 ...

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### 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 ...

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### 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 ...

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### 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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### 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 ...