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Results tagged with springer-fibres
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user 31327
8
votes
0
answers
265
views
A Lie-theoretic question regarding $B\ltimes \mathfrak{g}/\mathfrak{b}$
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 …
- 1,856
4
votes
0
answers
258
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Families of Hessenberg varieties for $GL_n$
In short, the question is
What do we know about the sheaf $\pi_*\underline{\bar{\mathbb{Q}}_{\ell}}$ given by the family of (very original, see below) Hessenberg varieties for $GL_n$? As a sum of …
- 1,856
4
votes
0
answers
221
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Centralizer action on components of Springer fibers
Let $G$ be a complex adjoint group. Let $u\in G$ be unipotent. The group $A(u):=\pi_0(Z_G(u))$ acts on the set of components of the Springer fiber $\mathcal{B}_u$, the variety of Borel subgroups that …
- 1,856
4
votes
0
answers
280
views
Computing Springer action on the homology of affine Springer fibers
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 …
- 1,856
3
votes
2
answers
607
views
counting points on nilpotent Springer fiber
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 …
- 1,856