7 citations · 10 across the 13 of their papers we have counts for
8 papers · 1 filter
On symmetric invariants of centralisers in reductive Lie algebras
D. Panyushev, A. Premet, O. Yakimova
Let be the centraliser of a nilpotent element in a finite dimensional simple Lie algebra of rank over an algebraically closed field of characteristic 0. We invest…
The index of representations associated with stabilisers
Dmitri I. Panyushev, Oksana S. Yakimova
Let be an algebraic group and a -module. The index of is the minimal codimension of the -orbits in the dual space . There is a general inequality, due to Vin…
Normalizers of ad-nilpotent ideals
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 $[\be,\be]$. We give several descriptions of t…
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…
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…