19 citations · 133 across the 72 of their papers we have counts for
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Weight posets associated with gradings of simple Lie algebras, Weyl groups, and arrangements of hyperplanes
Dmitri I. Panyushev
The set of weights of a finite-dimensional representation of a reductive Lie algebra has a natural poset structure ("weight poset"). Studying certain combinatorial problems related…
Antichains in weight posets associated with gradings of simple Lie algebras
Dmitri I. Panyushev
For a reductive Lie algebra and a simple finite-dimensional -module , the set of weights of , , has a natural poset structure. We consider an…
On the orbits of a Borel subgroup in abelian ideals
Dmitri I. Panyushev
Let be a Borel subgroup of a semisimple algebraic group , and let be an abelian ideal of . The ideal is determined by certain…
On Lusztig's -analogues of all weight multiplicities of a representation
Dmitri I. Panyushev
Let be a complex semisimple Lie algebra. We obtain new properties of the -analogue of weight multiplicities in finite-dimensional representations of .…