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Éléments réguliers et représentations de Gelfand-Graev des groupes réductifs non connexes

Karine Sorlin (2004)

Bulletin de la Société Mathématique de France

Soient G un groupe algébrique réductif connexe défini sur 𝔽 q et  F l’endomorphisme de Frobenius correspondant. Soit σ un automorphisme rationnel quasi-central de G . Nous construisons ci-dessous l’équivalent des représentations de Gelfand-Graev du groupe G ˜ F = G F · 〈 σ 〉 , lorsque σ est unipotent et lorsqu’il est semi-simple. Nous montrons de plus que ces représentations vérifient des propriétés semblables à celles vérifiées par les représentations de Gelfand-Graev dans le cas connexe en particulier par rapport aux...

Equations of some wonderful compactifications

Pascal Hivert (2011)

Annales de l’institut Fourier

De Concini and Procesi have defined the wonderful compactification 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 on the ( - 1 ) -eigenspace...

Equidimensional actions of algebraic tori

Haruhisa Nakajima (1995)

Annales de l'institut Fourier

Let X be an affine conical factorial variety over an algebraically closed field of characteristic zero. We consider equidimensional and stable algebraic actions of an algebraic torus on X compatible with the conical structure. We show that such actions are cofree and the nullcones of X associated with them are complete intersections.

Equivariant degenerations of spherical modules for groups of type A

Stavros Argyrios Papadakis, Bart Van Steirteghem (2012)

Annales de l’institut Fourier

V. Alexeev and M. Brion introduced, for a given a complex reductive group, a moduli scheme of affine spherical varieties with prescribed weight monoid. We provide new examples of this moduli scheme by proving that it is an affine space when the given group is of type A and the prescribed weight monoid is that of a spherical module.

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Kostov, Vladimir (2001)

Serdica Mathematical Journal

Research partially supported by INTAS grant 97-1644We consider the variety of (p + 1)-tuples of matrices Aj (resp. Mj ) from given conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) such that A1 + . . . + A[p+1] = 0 (resp. M1 . . . M[p+1] = I). This variety is connected with the weak Deligne-Simpson problem: give necessary and sufficient conditions on the choice of the conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) so that there exist (p + 1)-tuples with trivial centralizers of matrices...

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