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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47 papers · 1 filter

math.RT2026

The index of subalgebras and strange coadjoint orbits

Dmitri I. Panyushev

For an algebraic group $Q$ with $Lie Q = q$ , we develop a method for estimating the index of a subalgebra $h$ in $q$ via the use of coadjoint…

math.RT2026

Near-derivations and their applications to Lie algebras

Dmitri Panyushev, Oksana Yakimova

E.B. Vinberg's theory of quasi-derivations of algebras is extended to a broader framework of near-derivations. This deepens connections between Poisson geometry and Lie theory. Alt…

math.RT2026

Horospherical splittings of $g$ and related Poisson commutative subalgebras of $S (g)$

Dmitri Panyushev, Oksana Yakimova

Let a Lie algebra $q$ be a linear sum of two complementary subalgebras $h$ and $r$ . We continue our investigations initiated in (J. London Math. Soc.…

math.RT2025

Invariants of twisted current algebras and related Poisson-commutative subalgebras

Dmitri Panyushev, Oksana Yakimova

Let q be a finite-dimensional Lie algebra and $θ$ an automorphism of q of order m. We extend $θ$ to an automorphism of the loop algebra of q and consider the fixed-point subalgebra…

math.RT2024

Projections of nilpotent orbits in a simple Lie algebra and shared orbits

Dmitri I. Panyushev

Let $G$ be a simple algebraic group with $g = L i e (G)$ and $O \subset g$ a nilpotent orbit. If $H$ is a reductive subgroup of $G$ with $L i e (H) = h$ ,…

math.RT2024★ 1 cited

Orbits and invariants for coisotropy representations

Dmitri I. Panyushev

For a subgroup $H$ of a reductive group $G$ , let $m \subset g^{*}$ be the cotangent space of $eH \in G / H$ . The linear action $(H : m)$ is the coisotropy rep…

math.RT2023

The Frobenius semiradical, generic stabilisers, and Poisson centre for nilradicals

Dmitri I. Panyushev

Let $g$ be a complex simple Lie algebra and $n$ the nilradical of a parabolic subalgebra of $g$ . We consider some properties of the coadjoint represen…

math.RT2022

Automorphisms of finite order, periodic contractions, and Poisson-commutative subalgebras of $S (g)$

Dmitri Panyushev, Oksana Yakimova

Let $g$ be a semisimple Lie algebra, $ϑ \in Aut (g)$ a finite order automorphism, and $g_{0}$ the subalgebra of fixed points of $ϑ$ .…

math.RT2022

Combinatorial and geometric constructions associated with the Kostant cascade

Dmitri I. Panyushev

Let $g$ be a complex simple Lie algebra and $b = t \oplus u^{+}$ a fixed Borel subalgebra. Let $Δ^{+}$ be the set of positive roots associated with…

math.RT2021

Commutative polarisations and the Kostant cascade

Dmitri I. Panyushev

Let $g$ be a complex simple Lie algebra. We classify the parabolic subalgebras $p$ of $g$ such that the nilradical of $p$ has a commutative…

math.RT2021

Projections of the minimal nilpotent orbit in a simple Lie algebra and secant varieties

Dmitri I. Panyushev

Let $G$ be a simple algebraic group with $g = Lie G$ and $O_{min} \subset g$ the minimal nilpotent orbit. For a $Z_{2}$ -grading $\mathfr…

math.RT2021

Periodic automorphisms, compatible Poisson brackets, and Gaudin subalgebras

Dmitri I. Panyushev, Oksana S. Yakimova

Let $g$ be a finite-dimensional Lie algebra. The symmetric algebra $S (g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborat…

math.RT2021

Nilpotent orbits and mixed gradings of semisimple Lie algebras

Dmitri I. Panyushev

Let $σ$ be an involution of a complex semisimple Lie algebra $g$ and $g = g_{0} \oplus g_{1}$ the related $Z_{2}$ -grading. We study relations…

math.RT2020

Reductive subalgebras of semisimple Lie algebras and Poisson commutativity

Dmitri I. Panyushev, Oksana S. Yakimova

Let $g$ be a semisimple Lie algebra, $h \subset g$ a reductive subalgebra such that $h^{⊥}$ is a complementary $h$ -submodule of $\…

math.RT2020★ 6 cited

Compatible Poisson brackets associated with 2-splittings and Poisson commutative subalgebras of $S (g)$

Dmitri Panyushev, Oksana Yakimova

Let $S (g)$ be the symmetric algebra of a reductive Lie algebra $g$ equipped with the standard Poisson structure. If ${\mathcal C}\subset\mathcal S(\m…

math.RT2019

Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications

Dmitri I. Panyushev

Let $g$ be a simple Lie algebra, $h$ a Levi subalgebra, and $C_{h} \in U (h)$ the Casimir element defined via the restriction of the Killing f…

math.RT2018★ 5 cited

Poisson-commutative subalgebras of $S (g)$ associated with involutions

Dmitri Panyushev, Oksana Yakimova

The symmetric algebra $S (g)$ of a reductive Lie algebra $g$ is equipped with the standard Poisson structure, i.e., the Lie-Poisson bracket. Poisson-commutative…

math.RT2018★ 2 cited

Abelian ideals of a Borel subalgebra and root systems, II

Dmitri I. Panyushev

Let $g$ be a simple Lie algebra with a Borel subalgebra $b$ and $Ab$ the set of abelian ideals of $b$ . Let $Δ^{+}$ be the corresponding set o…

math.RT2018

Semi-direct products involving $S p_{2 n}$ or $S p i n_{n}$ with free algebras of symmetric invariants

Dmitri I. Panyushev, Oksana S. Yakimova

This is a part of an ongoing project, the goal of which is to classify all semi-direct products $s = g ⋉ V$ such that $g$ is a simple Lie algebra…

math.RT2017

Abelian ideals and amazing roots

Dmitri I. Panyushev

Let $g$ be a simple Lie algebra with a Borel subalgebra $b$ . To any long positive root $γ$ , one associates two ideals of $b$ : the abelian ideal $I(γ)_…

math.RT2017

Takiff algebras with polynomial rings of symmetric invariants

Dmitri Panyushev, Oksana Yakimova

Extending results of Rais-Tauvel, Macedo-Savage, and Arakawa-Premet, we prove that under mild restrictions on the Lie algebra $q$ having the polynomial ring of symmetric…

math.RT2017★ 2 cited

Semi-direct products of Lie algebras and covariants

Dmitri Panyushev, Oksana Yakimova

The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $q$ is a thrilling and fascinating object. Symmetric invariants of $q$ (= $\mat…

math.RT2017★ 10 cited

On seaweed subalgebras and meander graphs in type D

Dmitri Panyushev, Oksana Yakimova

In 2000, Dergachev and Kirillov introduced subalgebras of "seaweed type" in $gl_{n}$ and computed their index using certain graphs, which we call type- $A$ meander gr…

math.RT2016★ 3 cited

Symmetric invariants related to representations of exceptional simple groups

Dmitri I. Panyushev, Oksana S. Yakimova

We classify the finite-dimensional rational representations $V$ of the exceptional algebraic groups $G$ with $g = Lie (G)$ such that the symmetric invariants of the se…

The index of subalgebras and strange coadjoint orbits

Near-derivations and their applications to Lie algebras

Horospherical splittings of g and related Poisson commutative subalgebras of S(g)

Invariants of twisted current algebras and related Poisson-commutative subalgebras

Projections of nilpotent orbits in a simple Lie algebra and shared orbits

Orbits and invariants for coisotropy representations

The Frobenius semiradical, generic stabilisers, and Poisson centre for nilradicals

Automorphisms of finite order, periodic contractions, and Poisson-commutative subalgebras of S(g)

Combinatorial and geometric constructions associated with the Kostant cascade

Commutative polarisations and the Kostant cascade

Projections of the minimal nilpotent orbit in a simple Lie algebra and secant varieties

Periodic automorphisms, compatible Poisson brackets, and Gaudin subalgebras

Nilpotent orbits and mixed gradings of semisimple Lie algebras

Reductive subalgebras of semisimple Lie algebras and Poisson commutativity

Compatible Poisson brackets associated with 2-splittings and Poisson commutative subalgebras of S(g)

Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications

Poisson-commutative subalgebras of S(g) associated with involutions

Abelian ideals of a Borel subalgebra and root systems, II

Semi-direct products involving Sp2n​ or Spinn​ with free algebras of symmetric invariants

Abelian ideals and amazing roots

Takiff algebras with polynomial rings of symmetric invariants

Semi-direct products of Lie algebras and covariants

On seaweed subalgebras and meander graphs in type D

Symmetric invariants related to representations of exceptional simple groups

Horospherical splittings of $g$ and related Poisson commutative subalgebras of $S (g)$

Automorphisms of finite order, periodic contractions, and Poisson-commutative subalgebras of $S (g)$

Compatible Poisson brackets associated with 2-splittings and Poisson commutative subalgebras of $S (g)$

Poisson-commutative subalgebras of $S (g)$ associated with involutions

Semi-direct products involving $S p_{2 n}$ or $S p i n_{n}$ with free algebras of symmetric invariants