On irreducible sl (2, R) - modules and sl 2-triples.
On Ol'shanskii's semigroup.
On rational solutions of Yang-Baxter equation for sl(n).
On Root Systems.
On subsemigroups of semisimple Lie groups
On the center of . (Sur le centre de .)
On the characteristic polynomials of orbital varieties
On the Chevalley restriction theorem.
On the combinatorics of Kac's asymmetry function
We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac--Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function. The latter is...
On the complicatedness of the pair (g,K).
On the geometry of conjugacy classes in classical groupes.
On the ghost centre of Lie superalgebras
We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.
On the nilpotent residuals of all subalgebras of Lie algebras
Let denote the class of nilpotent Lie algebras. For any finite-dimensional Lie algebra over an arbitrary field , there exists a smallest ideal of such that . This uniquely determined ideal of is called the nilpotent residual of and is denoted by . In this paper, we define the subalgebra . Set . Define for . By denote the terminal term of the ascending series. It is proved that if and only if is nilpotent. In addition, we investigate the basic properties of a Lie algebra...
On the regularity and rationality of certain elements of finite order in Lie groups.
On the structure of an ...-stratified generalized Verma module over Lie algebra sl(n, C).
On the variety of lagrangian subalgebras, I
On the variety of lagrangian subalgebras, II
On Whitehead's second lemma for Lie algebras.
On Witten multiple zeta-functions associated with semisimple Lie algebras I
We define Witten multiple zeta-functions associated with semisimple Lie algebras , of several complex variables, and prove the analytic continuation of them. These can be regarded as several variable generalizations of Witten zeta-functions defined by Zagier. In the case , we determine the singularities of this function. Furthermore we prove certain functional relations among this function, the Mordell-Tornheim double zeta-functions and the Riemann zeta-function. Using these relations, we prove...
Order relations on conjugacy classes and the Kazhdan-Lusztig map.