7 citations · 10 across the 13 of their papers we have counts for
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Ideals of Heisenberg type and minimax elements of affine Weyl groups
Dmitri I. Panyushev
We consider ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra. The goal of this paper is two-fold. First, we study the ad-nilpotent ideals lying inside the Heisenbe…
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…
Short antichains in root systems, semi-Catalan arrangements, and B-stable subspaces
Dmitri I. Panyushev
Let $\be$ be a Borel subalgebra of a complex simple Lie algebra $\g$. An ideal of $\be$ is called ad-nilpotent, if it is contained in $[\be,\be]$. The generators of an ad-nilpotent…
Long Abelian ideals
Dmitri I. Panyushev
We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the…
Ad-nilpotent ideals of a Borel subalgebra: generators and duality
Dmitri I. Panyushev
It was shown by Cellini and Papi that an ad-nilpotent ideal determines certain element of the affine Weyl group, and that there is a bijection between the ad-nilpotent ideals and t…