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I understand how weights are defined for a Lie algebra representation. How are weight spaces defined for a Lie group action (with respect to a fixed torus)? I know this is a very embarrassing basi …

What i understand about strata for the nullcone is this: (from Mumford's "Geometric Invariant Theory" and Hesselink's paper "Desingularizations of Varieties of Nullforms") ADDED BY DAVID SPEYER In th …

Here's a question I've been thinking about, it's a curiosity that I don't know how to answer. There could be a simple counterexample, or it could be true and I don't know how difficult it would be to …

What results are known about representations of reductive groups over finite rings in general? Here by finite rings I usually mean an algebra over $F_q$, I guess. I know Lusztig has a paper generali …

The following is from this talk: http://www.maths.usyd.edu.au/u/anthonyh/piecestalk.pdf, Slide 14. The Springer correspondence gives bijections SO2n+1 \ N(so2n+1) ↔ {(μ; ν) | μi ≥ νi − 2, νi ≥ μi+1 …

How would one classify the strata for the standard nilpotent cone for $GL_{k}(\mathbb{C})$, using the definition from Hesselink's paper "Desingularizations of Varieties of Nullforms"? I know that they …

I understand the ordinary Springer correspondence gives a bijection between orbits in the nilpotent cone for the adjoint representation and irreducible representations of the Weyl group, through actio …

How do you compute in characteristic $0$, intersection cohomology of partial flag varieties (corresponding to a fixed partition $\lambda$)? I understand the answer involves Kazhdan-Lusztig polynomials …

What is a "nice" way of choosing coset representatives for the symplectic group $Sp_{2k}(\mathbb{C})$ in the general linear group $GL_{2k}(\mathbb{C})$?

I understand if a partition $\lambda$ has all parts even and all multiplicities even, then the nilpotent orbit corresponding to $\lambda$ splits up into two orbits. By the nilpotent orbit correspondin …

I have 2 questions - the first is what the title refers to, and the second is something I want a reference on (I thought I'd include them in one post since they are very strongly related). Sorry this …

Let $G$ be a reductive group over a finite field (i.e. finite groups over lie type). The case I am most interested in is $G=GL_{n}(\mathbb{F}_{q})$; other classical groups are also interesting I think …

I was wondering if someone knows a good reference for the representation theory of the hyper-octahedral group $G$. The hyper-octahedral group $G$ is defined as the wreath product of $C_2$ (cyclic grou …

Background: I am focusing on $G=GL_{2}(\overline{\mathbb{F_q}})$ here. If you wonder why I am interested in this, I am trying a problem relating to the Deligne-Lusztig varieties defined over local rin …

Background: I'm trying a problem on representations of reductive groups over various finite rings towards which this is very relevant (what I want to do is a very specialized case of this problem, and …