D. Panyushev

activity

19992026

most citedSymmetric pairs and associated commuting varieties

19 citations · 133 across the 72 of their papers we have counts for

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9 papers · 1 filter

math.CO2018

Glorious pairs of roots and Abelian ideals of a Borel subalgebra

Dmitri I. Panyushev

Let $g$ be a simple Lie algebra with a Borel subalgebra $b$ . Let $Δ^{+}$ be the corresponding (po)set of positive roots and $θ$ the highest root. A pair $\{η,η'\}…

math.CO2014★ 1 cited

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…

math.CO2014

Antichains in weight posets associated with gradings of simple Lie algebras

Dmitri I. Panyushev

For a reductive Lie algebra $h$ and a simple finite-dimensional $h$ -module $V$ , the set of weights of $V$ , $P (V)$ , has a natural poset structure. We consider an…

math.CO2010

Abelian ideals of a Borel subalgebra and subsets of the Dynkin diagram

Dmitri I. Panyushev

Let $g$ be a simple Lie algebra and $A b (g)$ the set of Abelian ideals of a Borel subalgebra of $g$ . In this note, an interesting connection between $A b (g)$ and the subsets of the D…

math.CO2008★ 1 cited

Properties of weight posets for weight multiplicity free representations

Dmitri I. Panyushev

We study weight posets of weight multiplicity free (=wmf) representations $R$ of reductive Lie algebras. Specifically, we are interested in relations between $dim R$ and the numbe…

math.CO2007

On orbits of antichains of positive roots

Dmitri I. Panyushev

For any finite poset P, there is a natural operator $X$ acting on the antichains of P. We discuss conjectural properties of this operator for some graded posets associated with irr…