19 citations · 133 across the 72 of their papers we have counts for
4 papers · 1 filter
Semi-direct products of Lie algebras and their invariants
Dmitri I. Panyushev
The goal of this paper is to extend the standard invariant-theoretic design, well-developed in the reductive case, to the setting of representation of certain non-reductive groups.…
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…
Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals
Dmitri I. Panyushev
We introduce two polynomials (in ) associated with a finite poset that encode some information on the covering relation in . If is a distributive lattice, and hence $…