7 citations · 10 across the 13 of their papers we have counts for
17 papers
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…
The poset of positive roots and its relatives
Dmitri I. Panyushev
Let be a root system with a subset of positive roots, . We consider edges of the Hasse diagrams of some posets associated with . For each edge one naturally defines i…
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…
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…