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Pardon if this is well known. Suppose I have a (say complex) connected reductive group $G^{\vee}$ with the $\tilde{\Delta}=\Delta\cup\{\alpha_0\}$ being the simple roots plus the negative highest root …

About Definition 2.3 in Character Sheaves I: We have the usual $G$, $B$, $T$, Weyl group $W$ and roots $R$. Lusztig wrote down a definition of $R_{\mathcal{L}}$ as: $$R_{\mathcal{L}}=\{\alpha\in R\;|\ …

This could well be a question for reading suggestion. Hope it's not too bad and thanks a lot. So the question is as in the title. What are the relations between the notion of unipotent cuspidal repre …

I wish to ask about good examples of new applications of Lusztig's theory of character sheaves (and subsequent development, but excluding generalized Springer theory) back to the theory of characters …

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 represe …

I am wondering if there is a theorem of Shalika germ (as below) for local function field, for both the group version or the Lie algebra version, probably under assumption on the characteristic to be v …

Computing $p$-adic orbital integral I come to the following question. My ground field $k$ is the residue field of a non-arch local field, i.e. a finite field. I am happy to put any assumption on $\tex …

Let $G$ be a reductive group over a local non-arch field $F$. For convenience let's assume $G$ has anisotropic center (or even that $G$ is semisimple if preferred). Let $x$ be any point in the buildin …

Lusztig defined (in Sec. 5, also Sage) a Springer action of the affine Weyl group on the homology of affine Springer fibers (Iwahori one, i.e. in an affine flag variety). In the regular semisimple unr …

I am interested in the detailed computation of the generalized Springer theory for spin groups (type B or D). In the last sentence in Section 14 of Lusztig's Intersection cohomology complex on a reduc …

So the essential question is: How should we think about, or if possible compute, the semisimple support of a cuspidal character sheaf? For example, let $G=SL_2$. We have the cuspidal characte …

I think the following is true, but haven't came up with a proof myself. Thanks in advance! Let $G$ be a semisimple (to avoid more words) algebraic group over $\mathbb{C}$. Write $F=\mathbb{C}((t))$ a …

Let $G$ be an connected reductive group over finite field $k$. I will assume that $\text{char}(k)$ is very good for $G$ (or even larger, if preferred). Let $B\subset G$ be a Borel subgroup defined ove …

I am stuck on a seeming elementary Lie-theoretic question arising from a study of components of affine Springer fibers. Will be very grateful if somebody would like to share some insight, or intereste …

I am interested in understanding a situation in (classical, not $p$-adic) local Langlands for $\mathrm{GL}_p(\mathbb{Q}_p)$. An example of it is as follows: Let $F=\mathbb{Q}_2$ and $E$ be the splitti …