# Tagged Questions

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

1answer
342 views

### On the symmetric group of 2^n elements

Consider the set $X_1^n=\{1,2,...,2^n\}$. Then define $X_2^n$ to be the set of two element subsets of $X_1^n$. I will construct $X_i$ by induction on $i$. $X_i^n$ is the set of two element ...
1answer
139 views

0answers
215 views

### Geometric Satake and Restriction

The Geometric Satake correspondence (due to Lusztig, Ginzburg, Mirkovic-Vilonen) relates perverse sheaves on the Loop Group $\hat{G}$ (with their convolution product) to the Representations of the ...
2answers
235 views

### What are the special parahoric subgroups in unitary groups?

Let $L$ be a $p$-adic field and let $L'/L$ be a quadratic extension. Let $U_{L'/L}(n)$ be a quasi-split unitary group of $n\times n$ matrices with entries in $L'$. I'm curious about what the special ...
4answers
1k views

### Why do people study representations of 3-manifold groups into $SL(n,\mathbb{C})$?

Varieties of representations and characters of $3$-manifold groups in $SL(2,\mathbb{C})$ have been intensively studied. They have provided tools to identify geometric structures on manifolds, and are ...
1answer
178 views

### How fine an invariant of a representation is its quotient singularity?

This is a refinement of a question asked on MSE. Let $G$ be a finite group and let $V$ be a finite-dimensional faithful complex representation of $G$. Consider $V$ as an affine complex variety. In ...
0answers
106 views

0answers
81 views

### How to write down solutions of Yang-Baxter equations for $sl_3$ explicitly?

In the paper, Stolin classifies all quasi-Frobenius subalgebras of $sl_3$. How to write down solutions of Yang-Baxter equations for $sl_3$ explicitly using these quasi-Frobenius subalgebras? Thank you ...
1answer
274 views

### what is the injective hull of indecomposable module of preprojective algebra

Let $Q$ be a ADE type quiver and $s_i$ ($i$ runs through the vertices of $Q$) be the simple $\Lambda$-module with 1-dimensional vector space at vertex $i$ and zero-dim at other vertices. Here $\Lambda$...
1answer
201 views

0answers
84 views

### Quantum Groups and quantum spaces - From algebra to Analysis

My question will be about the non-standard quantum projective space $\mathcal{A}_q(\mathbb{CP}^n(c,d))$ introduced by Dijkhuizen and Noumi. I want to see this algebra now on a von Neumann algebraic ...
1answer
152 views

### Super-plethysm?

Let $U$ be a representation of $S_m$ and $V$ a representation of $S_n$. Then the representation $\operatorname{Ind}_{S_m\wr S_n}^{S_{mn}}(U^{\otimes{n}}\otimes V)$ has a nice interpretation in terms ...
0answers
71 views

### 2-functoriality of equivariant derived categories

I am wondering about the 2-functoriality in equivariant derived categories, and I hope that someone can clarify... (apologies if this is a stupid question) For the more precise formulation, recall ...
1answer
80 views

### presentation for a nilpotent group associated to the square of a coxeter element

This question is related to one asked earlier about inductive presentations of unipotent radicals in Kac-Moody groups. Let $\Gamma$ be a coxeter diagram --- i.e. an unoriented graph with $r$ vertices ...
0answers
90 views

1answer
115 views

### indecomposable modules restricted from $gl_n$ to $sl_n$

Let K be an algebraic closed field, $gl_n$ be the general linear Lie algebra over K, and $sl_n$ be the special linear Lie algebra. Let $\chi\in gl_n^*$. Let $U_\chi(gl_n)$ be the corresponding reduced ...
0answers
178 views

### Mixed up by definitions of mildly mixing

Here are two setup where the notion of "mildly mixing" comes up: for representations and for group acting by measure preserving transformations (see definitions below). Since a natural class of ...
0answers
118 views

### nilpotent orbits in p-adic period domain

I am going to prove an analogue of the W. Schmid nilpotent orbit theorem in p-adic Hodge theory. It seems to me that a similar limit of filtration by slopes of isocrystals should be semistable. I am ...
1answer
206 views

### inductive construction of unipotent radicals

Consider a directed coxeter diagram $\vec{\Gamma}$, i.e. a finite graph where each edge is decorated with one of the integer weights $\big\{3,4,6\big\}$ and those edges with weights $4$ or $6$ are ...
1answer
57 views