Elementary proof of a theorem of Bruhat-Tits-Rousseau and of a theorem of Tits
Éléments réguliers et représentations de Gelfand-Graev des groupes réductifs non connexes
Soient un groupe algébrique réductif connexe défini sur et l’endomorphisme de Frobenius correspondant. Soit un automorphisme rationnel quasi-central de . Nous construisons ci-dessous l’équivalent des représentations de Gelfand-Graev du groupe , lorsque 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...
Éléments unipotents et sous-groupes paraboliques de groupes réductifes. I.
Elliptic subgroups of linear groups over a valued field. (Sous-groupes elliptiques de groupes linéaires sur un corps valué.)
Embeddings of finite classical groups over field extensions and their geometry.
Embeddings of maximal tori in orthogonal groups
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic to contain a maximal torus of a given type.
Embeddings of U3 (8), Sz (8) and the Rudvalis group in algebraic groups of type E7.
Endlich präsentierte arithmetische Gruppen und K2 über Laurent-Polynomringen.
Endliche arithmetische Untergruppen der GLn.
Endliche Spiegelungsgruppen, die als Weylgruppen auftreten.
Equations defining Schubert varieties and Frobenius splittings of diagonals
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
Equations of some wonderful compactifications
De Concini and Procesi have defined the wonderful compactification of a symmetric space where is a complex semisimple adjoint group and the subgroup of fixed points of by an involution . It is a closed subvariety of a Grassmannian of the Lie algebra of . In this paper we prove that, when the rank of is equal to the rank of , the variety is defined by linear equations. The set of equations expresses the fact that the invariant alternate trilinear form on vanishes on the -eigenspace...
Equidimensional actions of algebraic tori
Let 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 compatible with the conical structure. We show that such actions are cofree and the nullcones of associated with them are complete intersections.
Equivariant degenerations of spherical modules for groups of type
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 and the prescribed weight monoid is that of a spherical module.
Errata-Corrigé : «Cohomologie de et valeurs de fonctions zêta aux points entiers»
Erratum à l’article : «Représentations modulaires de en caractéristique , corps -adique, »
Erratum: Multiplicative stability for the cohomology of finite Chevalley groups. Math. Helvetici 63 (1988), 108-113.
Espaces homogenes spheriques.
Espaces principaux homogènes localement triviaux