Irreducible representations of Lie algebras of reductive groups and the Kac-Weisfeiler conjecture.
Maticové Lieovy grupy a Lieovy algebry
Moore-Penrose inverse, parabolic subgroups, and Jordan pairs.
MOP -- algorithmic modality analysis for parabolic actions.
Naive boundary strata and nilpotent orbits
We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups , , and .
Nilpotency in Classical Groups over a Field of Characteristic 2.
Nilpotent Classes and Sheets of Lie Algebras in Bad Characteristic.
On irreducible sl (2, R) - modules and sl 2-triples.
On normal abelian subgroups in parabolic groups
Let be a reductive algebraic group, a parabolic subgroup of with unipotent radical , and a closed connected subgroup of which is normalized by . We show that acts on with finitely many orbits provided is abelian. This generalizes a well-known finiteness result, namely the case when is central in . We also obtain an analogous result for the adjoint action of on invariant linear subspaces of the Lie algebra of which are abelian Lie algebras. Finally, we discuss a connection...
On spherical nilpotent orbits and beyond
We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s -groups. This yields a description of spherical...
On the Cartan subalgebras of Lie algebras over small fields.
On the complicatedness of the pair (g,K).
On the principal bundles over a flag manifold.
Orbites d'un groupe algébrique dans l'espace des idéaux rationnels d'une algèbre enveloppante
Polarization in the Classical Groups.
Polycyclic groups, Lie algebras and algebraic groups.
Produit tensoriel de matrices, homologie cyclique, homologie des algèbres de Lie
On munit, naturellement, d’un surproduit l’algèbre extérieure de l’homologie cyclique d’une -algèbre commutative ( étant un corps de caractéristique zéro) à l’aide du produit de Loday-Quillen. On munit d’un surproduit l’homologie de l’algèbre de Lie du groupe linéaire général de à l’aide du produit tensoriel de matrices. On montre que l’isomorphisme d’algèbres de Hopf de Loday-Quillen est compatible avec les surproduits définis ci-dessus. On obtient ainsi une interprétation du produit de Loday-Quillen,...
Proof of Verma's Conjecture on Weyl's Dimension Polynomial.
Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras.
We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements. Parabolic subalgebras of a semisimple Lie algebra are not always quasi-reductive (except in types A or C by work of Panyushev). The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo,...
Series of nilpotent orbits.