# Tagged Questions

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

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### Points of failure in definition of X- and A-moduli spaces for arbitrary G

In their work [0] on defining notions of higher Teichmüller space for local systems on surfaces, Fock and Goncharov require split reductive Lie groups, and sometimes also require simple-connectedness. ...
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### Is it true that irreducible smooth representations of $G_2(F)$ are self-dual?

Let $G_2$ be the split exceptional group of type $G_2$ and $F$ be a p-adic field. Is it true that every irreducible smooth representation of $G_2(F)$ is self-contragradient? If the answer is Yes, can ...
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### Examples to keep in mind while reading the book 'The Admissible Dual…' by Bushnell and Kutzko and the importance of Interwining of representations

I am a beginner in the field of representation theory. I was reading the book 'The Admissible Dual of $GL(N)$ Via Compact Open Subgroups' by Bushnell and Kutzko. Let me first describe the book a ...
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### Integral representation of adjoint L-factor for GL(2)

My question is about a local computation in the paper of Gelbart and Jacquet, "A relation between automorphic representations of GL2 and GL3", from 1978. Let $\sigma$ be an irreducible smooth complex ...
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### positivity of semicanonical basis

Given a quiver $Q$, there is an algebra isomorphism from $U\frak{n}$ to $\mathcal{M}\subset \sum_{v}\text{Const}(\Lambda_v)^{G_v}$ by Lusztig's construction. Fro each $Z\in \text{Irr}(\Lambda_v)$. ...