Orders of Lie algebras over domains
Orthogonal Gelfand-Zetlin algebras. I.
Paramétrisation d'orbites dans les nappes de Dixmier admissibles
Parametrisierung von Konjugationsklassen in sln.
Prehomogeneous spaces associated with nilpotent orbits in simple real Lie algebras and and their relative invariants.
Projective reparametrization of homogeneous curves
We study the conditions when locally homogeneous curves in homogeneous spaces admit a natural projective parameter. In particular, we prove that this is always the case for trajectories of homogeneous nilpotent elements in parabolic spaces. On algebraic level this corresponds to the generalization of Morozov–Jacobson theorem to graded semisimple Lie algebras.
Proof of the Parthasarathy-Ranga Rao-Varadarajan conjecture.
Proof of Verma's Conjecture on Weyl's Dimension Polynomial.
Properties of a 29-Dimensional Simple Lie Algebra of Characteristics Three.
Prym-Tjurin varieties and the Hitchin map.
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 The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo,...
Rational tori, semisimple orbits and the topology of hyperplane complements.
Recognizing cluster algebras of finite type.
Regular Elements of Finite Reflection Groups.
Relation between invertibility of Casimir operators and semisimplicity of quadratic Lie superalgebras.
Représentations indécomposables
Restriction to Levi subalgebras and generalization of the category
The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple.
Ringel-Hall algebras of hereditary pure semisimple coalgebras
We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.
Root Systems and Elliptic Curves
Root systems and hypergeometric functions. I