Questions tagged [springer-fibres]
The springer-fibres tag has no usage guidance.
16
questions with no upvoted or accepted answers
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Two-sided cells, special nilpotent orbits and special representations
Let $\mathfrak{g}$ be a complex semisimple Lie algebra. This question concerns three classical objects of representation theory: the two-sided Kazhdan-Lusztig cells of the Weyl group $W$ of $\mathfrak{...
8
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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 ...
6
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278
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Springer fibers and Weyl group
Let $\pi:\tilde{\mathfrak{g}}\rightarrow\mathfrak{g}$ the Grothendieck-Springer resolution of a semisimple Lie algebra $\mathfrak{g}$, over $\mathbb{C}$.
We know it's a small map, and that $\pi_{*}\...
5
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184
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Homeomorphisms of Springer fibers
Let $V$ be a complex $n$-dimensional vector space and denote by ${\cal F}$ its space of complete flags. Let $g \in Gl(V)$ be unipotent and consider the Springer fiber ${\cal F}_g$ of its fixed points ...
4
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123
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Relations between double coinvariants and affine Springer fibers
Diagonal coinvariants have an interpretation from https://arxiv.org/abs/math/0201148 in terms of the Hilbert scheme.
There are two recent papers https://arxiv.org/pdf/1801.09033.pdf and https://arxiv....
4
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118
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Intersection of components in Springer fibre of type A
From the standard results on Springer fibers of type A, we know that given a Springer fiber, say $\mathcal{B}_\lambda,$ its irreducible components are all equidimensional and parametrized by standard ...
4
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253
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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 ...
4
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213
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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 ...
3
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291
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Understanding the proof of the Springer correspondence
Let $G$ be a connected reductive group over an algebraically closed field $k$ with Weyl group $W$.
Let
$$
\mathcal{S} = R\pi_*\mathbb{Q}_\ell[\dim \mathcal{N}]
$$
be the Springer sheaf, where $\...
3
votes
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answers
267
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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 ...
2
votes
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85
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Multiplicities of components of a Springer fibre
Given a Springer fibre of type A, are multiplicities of its irreducible components known in general, or at least in the special cases of two-row/hook types?
By multiplicities I mean considering a ...
2
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162
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Are parabolic Springer fibers equal dimensional?
Let $G$ be a simple algrbraic group ( of type BCDEFG ) over the complex number $\mathbb{C}$, let $P$ be a parabolic subgroup of $G$, suppose we have a resolution of singularities $\mu: T^*(G/P)\to \...
2
votes
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180
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Springer sheaf and Deligne-Lusztig induction
Let $G=Gl_n$ be the general linear group over the algebraic closure of a finite field $\overline{\mathbb{F}}_q $ and let $F:G \to G$ be the standard Frobenius. On $G$ there is the Springer (perverse) ...
2
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165
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Counting points of parabolic Springer fibers
Let $G$ be a reductive group over an (algebraically closed ) field. To each parabolic subgroup $P \subseteq G$ and $x \in G$ we can consider two types of partial Springer fibers associated to it :
$$1)...
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59
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Affine Springer fibers for symmetric spaces
Springer fibers are defined to be the varieties of "isotropic" full flags which are fixed by a certain element in the symmetric space. In a similar manner, affine Springer fibers can be ...
0
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Extension of a type A Springer fibre
Given a decomposition $p=(p_1,\dots,p_n)$ of $n$, one can associate its corresponding
partial flag variety $$\mathcal{B}_p=\{F=(0=F_0\subset F_1\subset \dots \subset F_n=\mathbb{C}^n) \mid \dim F_i/F_{...