# Tagged Questions

Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.

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### Deformation of a Hopf algebra

A deformation of a Hopf algebra is defined as follows. On page 171 of the book a guide to quantum groups, Remark 2, it is said that Any deformation of a Hopf algebra $A$ as a bialgebra is ...
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### “Diagonalizing” Littlewood-Richardson coefficients

Let's consider the Littlewood-Richardson coefficients $c^{\lambda}_{\mu \nu}$ so that $$V_\mu \otimes V_\nu = \bigoplus_\lambda V_\lambda^{\oplus c^{\lambda}_{\mu \nu}}$$ ...
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### Order of metaplectic operator

I have a weak background on this subject. Suppose $S$ be a $2m \times 2m$ symplectic matrix of order $n$. Suppose $W_S$ be the corresponding metaplectic operator on $\mathcal{S}(\mathbb{R}^m)$, the ...
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### Cartan subspaces for general algebraic representations

So I feel like asking the following likely open-ended question: What good generalizations of the notion of Cartan subspace do we have? To be precise, let $G\curvearrowright V$ be an algebraic ...
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### Hopfian modules

My question is slightly motivated by basic results in linear algebra, for example, that if $F$ is a field then a surjective linear map $F^n \rightarrow F^n$ is injective. More generally, any ...
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### Is the direct sum in Maschke's Theorem an orthogonal decomposition?

I am reading a paper on coding theory, and it uses a statement, which was claimed to be a reformulation of Maschke's Theorem. But I felt that was false... Let's say $\mathcal(V):=\mathcal{F}_2^n$ is ...
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### Could Partial Tiltings be studied as Almost Complete Tiltings?

The first part of what follows is a brief recap of the definitions, setting and motivations for my questions. Experts can find the questions at the end. Here $k$ denotes an algebraically closed ...
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### Explicit formulas for certain elements in $Z(U(\mathfrak{gl_n}))$

Let $\lambda$ be a partition with $\leq n$ rows and let $L_{\lambda}$ be the corresponding irreducible representation of ${\rm GL}_n(\mathbb{C})$. Let $e_m(X_1,\dots,X_n)$ be the $m$th elementary ...
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### Degree of irreducible representations of a finite cyclic group over $\mathbb{Q}_p$

Let $p$ be a prime and $\mathbb{Q}_p$ denotes the $p$-adic numbers. Is it true that the degree of the nontrivial $\mathbb{Q}_p$-irreducible representations of a cyclic group of order $p^n$ is ...