7 citations · 10 across the 13 of their papers we have counts for
8 papers · 1 filter
An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras
Dmitri I. Panyushev
Let $\g$ be a simple Lie algebra of type A or C. We show that the coadjoint representation of any seaweed subalgebra of $\g$ has some properties similar to that of the adjoint repr…
On Invarinat Theory of -groups
Dmitri I. Panyushev
This paper is a contribution to Vinberg's theory of -groups, or in other words, to Invariant Theory of periodically graded semisimple Lie algebras. One of our main tools is Spri…
Regions in the dominant chamber and nilpotent orbits
Dmitri I. Panyushev
We give a geometric description for the dominant characteristic of a nilpotent orbit in an arbitrary finite-dimensional rational G-module. In particular, we obtain a generalization…
Some amazing properties of spherical nilpotent orbits
Dmitri I. Panyushev
Let $\g$ be simple Lie algebra. We give a conceptual proof for the fact that the nilpotent orbits of height 3 are spherical. It is shown that if the highest root of $\g$ is fundame…
Weight multiplicity free representations, -endomorphism algebras, and Dynkin polynomials
Dmitri I. Panyushev
-endomorphism algebras form an interesting class of associative algebras related to the adjoint representation of a semisimple Lie algebra . These algebras were r…
The index of a Lie algebra, the centraliser of a nilpotent element, and the normaliser of the centraliser
Dmitri I. Panyushev
In this paper, we study the index for several natural classes of non-reductive subalgebras of semisimple Lie algebras. Namely, we look at parabolic subalgebras, centralisers of nil…