# Tagged Questions

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

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### Stable equivalences preserving injective dimension

Let $A,B$ be two finite dimensional connected algebras and $F$ be a stable equivalence between their stable module categories (module category modulo projectives). Are there some natural conditions ...
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### Properties of non-abelian characters

I'm looking for some (short of) non-abelian generalization of the following result: Let $G$ be a finite abelian group and let $f$ be a function on $G$ with values in some field of characteristic ...
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### Representation of of $SO(3)$ in the vector space $V = \mathbb C^{2S+1}$

Certain part in my textbook implies that a representation of $SO(3)$ in the vector space $V = \mathbb C^{2S+1}$, where $S \in \mathbb Z$, is possible. I am trying to find a path that leads to this ...
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### Alternative proof : Group algebra contains all irreducible G-modules.

It is well-known that the group algebra $F[G]$ is a direct sum of irreducible $G$-modules. The proof in my text book is as follows Write $F[G] = \oplus_{i=1}^n V_i$, where $V_i$ is a set of ...
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### Equivalent definitions of semisimplicity of finite dimensional modules

Let $A$ be a finite dimensional $k$-algebra, and let $V$ be a finite dimensional $A$-module. How do we show that $V$ is semisimple (i.e. is the direct sum of simple submodules) if every maximal ...
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### The representation of $SU(2)$ as a polynomial function on $\mathbb C^2$

Let $A$ element of $SU(2)$ and $p$ a polynomial function of fixed degree $l$ on $\mathbb C^2$ (in other words, $p \in P_l(\mathbb C^2)$), then the polynomial representation of $A$ in $P_l(\mathbb C^2)$...
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### Relation between integrable representations and highest weight representations.

Let $g$ be a simple Lie algebra and $U_q(g)$ the corresponding quantum group. What are the relation between integrable representations and highest weight representations of $U_q(g)$? Are all highest ...