Embeddings of finite classical groups over field extensions and their geometry.
Faisceaux caractères
Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups
We provide partial results towards a conjectural generalization of a theorem of Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields or function fields) that implies, in low dimensions, both polynomial isoperimetric inequalities and finiteness properties. As a tool in our proof, we establish polynomial isoperimetric inequalities and finiteness properties for certain solvable groups that appear as subgroups of parabolic groups in semisimple groups, thus generalizing a theorem of Bux....
Filtrations of cohomology modules for Chevalley groups
Gaussian Maps and Tensor products of irreducible representations.
Generalized quivers associated to reductive groups
We generalize the definition of quiver representation to arbitrary reductive groups. The classical definition corresponds to the general linear group. We also show that for classical groups our definition gives symplectic and orthogonal representations of quivers with involution inverting the direction of arrows.
Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres.
H*(C/B,L) for G of semi-simple rank 2
Imprimitive Maximal Subgroups of the Orthogonal, Special Orthogonal, Unitary and Special Unitary Groups.
Induced Modules and Extensions of Representations.
Invariant differential operators on symplectic Grassmann manifolds.
Invariants d'un sous-groupe unipotent maximal d'un groupe semi-simple
Soit un groupe algébrique semi-simple complexe, un sous-groupe unipotent maximal de , un tore maximal de normalisant . Si est un -module rationnel de dimension finie, alors opère sur l’algèbre des fonctions polynomiales sur ; la structure de -module de est décrite par la -algèbre des -invariants de . Cette algèbre est de type fini et multigraduée (par le degré de et le poids par rapport à ). On donne une formule intégrale pour la série de Poincaré de cette algèbre graduée....
Invariants of four subspaces
We consider problems in invariant theory related to the classification of four vector subspaces of an -dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.
Isocrystals with additional structure
L2 Cohomology and Warped Products and Arithmetic Groups.
L’azione del gruppo simplettico associata ad un’estensione quadratica di campi
Les nombres de Tamagawa de groupes semi-simples
Local Borcherds products
The local Picard group at a generic point of the one-dimensional Baily-Borel boundary of a Hermitean symmetric quotient of type is computed. The main ingredient is a local version of Borcherds’ automorphic products. The local obstructions for a Heegner divisor to be principal are given by certain theta series with harmonic coefficients. Sometimes they generate Borcherds’ space of global obstructions. In these particular cases we obtain a simple proof of a result due to the first author: Suppose...
Minimal Singularities in GLn.
Minkowski's Successive Minima and the Zeros of a Convexity-Function.