Tensor products of finite and infinite dimensional representations of semisimple Lie algebras
The BGG diagram for contact orhogonal geometry of even dimension
The catenarity of the positive part of the quantized enveloping algebra of a simple Lie algebra of type . (La caténarité de la partie positive de l'algèbre enveloppante quantifiée de l'algèbre de Lie simple de type .)
The center of the universal enveloping algebra of a Lie algebra in characteristic
The closure diagrams for nilpotent orbits of real forms of .
The closure diagrams for nilpotent orbits of real forms of and .
The Enright Functor on the Bernstein-Gelfand-Gelfand Category ... .
The geometry of nilpotent coadjoint orbits of convex type in hermitian Lie algebras.
The groups of automorphisms of the Witt and Virasoro Lie algebras
Let be a Laurent polynomial algebra over a field of characteristic zero, the Lie algebra of -derivations of the algebra , the so-called Witt Lie algebra, and let be the Virasoro Lie algebra which is a -dimensional central extension of the Witt Lie algebra. The Lie algebras and are infinite dimensional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: , and give a short proof that .
The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras
The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.
The index of centralizers of elements of reductive Lie algebras.
The kernel of an homomorphism of Harish-Chandra
The Kostant partition functions for twisted Kac-Moody algebras.
The minimal orbit in a simple Lie algebra and its associated maximal ideal
The nil Hecke ring and Deodhar's conjecture on Bruhat intervals.
The normality of closures of orbits in a Lie algebra.
The Prime Spectrum of the Enveloping Algebra of a Reductive Lie Algebra.
The unitary dual of G2.
Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis.
Towards the Jantzen conjecture