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I am mostly likely only adding to the question here and not giving an answer. First, Are the unipotent cuspidal representations in Lusztig's 1977 work related to cuspidal charachter sheaves with non-t …

I think something very close to what is asked in the original question is explained by Haines, Kottwitz and A. Prasad in their review article.

The Kazhdan Lusztig map gives a correspondence between conjugacy classes of Weyl groups and nilpotent orbits. So, let $w$ be a conjugacy class and $N$ be the nilpotent orbit it gets mapped to under t …

Would "cominuscule Richardson orbits" be a satisfactory name ? It is basically a stringing together of adjectives that imply the two properties that were outlined in the question. A similar name (w/o …

Somewhat late, but let me answer my own question here by saying that using packages like CHEVIE (built for GAP) has been the most reliable way for me to compute j-induction. I'll leave Jim's answer as …

In Carter's book (Finite groups of Lie type), he reviews the truncated induction procedure (called j-operation in the text) of Macdonald-Lusztig-Spaltenstein in great detail for the classical Weyl gro …

I would like to know if there is an English version of a paper by Elashvili called "Centralizers of nilpotent elements in semisimple Lie algebras". If not, is there atleast an online version of the …

This is a question about two seemingly different notions of a left cell in a finite Weyl group and why they are the same. My question arose from reading a paper of W. McGovern titled "Left cells and d …

Let $G$ be an algebraic group. Choose a Borel subgroup $B$ and a maximal Torus $T \subset B$. Let $\Lambda$ be the set of weights wrt $T$ and let $\mathfrak{g}$ be the lie algebra of $G$. Now, conside …

In Representation Theory, the theme of the existence of a canonical basis has been explored quite a lot. I will limit myself in this question to the kind of canonical bases that arise from the Geometr …

This question is somewhat vaguely structured. But, I hope someone can make it more precise (or) it is indeed possible to answer it in the form that I am stating it.  Background : I recently chanced u …

My question is regarding a paper by R.W Richardson titled "Derivatives of invariant polynomials on a semisimple Lie Algebra" ** . In this paper, he reports on computations of the rank of the different …

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 Lan …

This is a very nice line of thinking! But I think the question, as stated, is imprecise. As is correctly pointed out in the question, the KL map takes you from nilpotent orbits in $\mathfrak{g}$ to …

In the study of adjoint orbits in a complex semi-simple lie algebra, there is a well known object known as a "sheet". These are the irreducible components of the union of orbits of the same dimension. …