Smooth components of Springer fibers

William Graham; R. Zierau

Displaying similar documents to “Smooth components of Springer fibers”

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

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Let $H \subset GL (V)$ be a connected complex reductive group where $V$ is a finite-dimensional complex vector space. Let $v \in V$ and let $G = {g \in GL (V) ∣ g H v = H v}$ . Following Raïs we say that the orbit $H v$ is if the identity component of $G$ is $H$ . If $H$ is semisimple, we say that $H v$ is for $H$ if the identity component of $G$ is an extension of $H$ by a torus. We classify the $H$ -orbits which are not (semi)-characteristic in many cases.

Limit formulas for groups with one conjugacy class of Cartan subgroups

Mladen Božičević (2008)

Annales de l’institut Fourier

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Limit formulas for the computation of the canonical measure on a nilpotent coadjoint orbit in terms of the canonical measures on regular semisimple coadjoint orbits arise naturally in the study of invariant eigendistributions on a reductive Lie algebra. In the present paper we consider a particular type of the limit formula for canonical measures which was proposed by Rossmann. The main technical tool in our analysis are the results of Schmid and Vilonen on the equivariant sheaves on...

Geometric Invariant Theory and Generalized Eigenvalue Problem II

Nicolas Ressayre (2011)

Annales de l’institut Fourier

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Let $G$ be a connected reductive subgroup of a complex connected reductive group $\hat{G}$ . Fix maximal tori and Borel subgroups of $G$ and $\hat{G}$ . Consider the cone $ℒ ℛ^{\circ} (G, \hat{G})$ generated by the pairs $(ν, \hat{ν})$ of strictly dominant characters such that $V_{ν}^{*}$ is a submodule of $V_{\hat{ν}}$ . We obtain a bijective parametrization of the faces of $ℒ ℛ^{\circ} (G, \hat{G})$ as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.

Equations of some wonderful compactifications

Pascal Hivert (2011)

Annales de l’institut Fourier

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De Concini and Procesi have defined the wonderful compactification $\bar{X}$ of a symmetric space $X = G / G^{σ}$ where $G$ is a complex semisimple adjoint group and $G^{σ}$ the subgroup of fixed points of $G$ by an involution $σ$ . It is a closed subvariety of a Grassmannian of the Lie algebra $𝔤$ of $G$ . In this paper we prove that, when the rank of $X$ is equal to the rank of $G$ , the variety is defined by linear equations. The set of equations expresses the fact that the invariant alternate trilinear form $w$ on $𝔤$ vanishes...

Rational points and Coxeter group actions on the cohomology of toric varieties

Gustav I. Lehrer (2008)

Annales de l’institut Fourier

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We derive a simple formula for the action of a finite crystallographic Coxeter group on the cohomology of its associated complex toric variety, using the method of counting rational points over finite fields, and the Hodge structure of the cohomology. Various applications are given, including the determination of the graded multiplicity of the reflection representation.