Let b be a Borel subalgebra of a simple Lie algebra g. Let Ab denote the set of all Abelian ideals of b. It is easily seen that any a âˆˆ Ab is actually contained in the nilpotent radical of b.â€¦ (More)

to Oksana INTRODUCTION This paper is a contribution to Vinberg's theory of Î¸-groups, or in other words, to Invariant Theory of periodically graded semisimple Lie algebras [Vi1],[Vi2]. One of our mainâ€¦ (More)

A seaweed subalgebra of a semisimple Lie algebra g is a generalization of the notion of parabolic subalgebra. In the case g = sl(V ), seaweed subalgebras were recently introduced by Dergachev andâ€¦ (More)

This definition goes back to J.Dixmier, see [Di, 11.1.6]. He considered index because of its importance in Representation Theory. The problem of computing the index may also be treated as part ofâ€¦ (More)

The ground field k is algebraically closed and of characteristic zero. Let g be a reductive algebraic Lie algebra. Classical results of Kostant [7] give a fairly complete invarianttheoretic pictureâ€¦ (More)

If a reductive group G acts on an algebraic variety X , then the complexity of X , or of the action, is the minimal codimension of orbits of a Borel subgroup. The concept of complexity has the originâ€¦ (More)

Let G be a simple algebraic group defined over an algebraically closed field k of characteristic zero. Write g for its Lie algebra. Let x âˆˆ g be a nilpotent element and GÂ·x âŠ‚ g the correspondingâ€¦ (More)

Let (P, 4) be an arbitrary finite poset. For any S âŠ‚ P, let Smin and Smax denote the set of minimal and maximal elements of S, respectively. An antichain in P is a subset of mutually incomparableâ€¦ (More)

The symmetric algebra of a (finite-dimensional) g-module V is the algebra of polynomial functions on the dual space V . Therefore one can study the algebra of symmetric invariants using geometry ofâ€¦ (More)