A. Petukhov

activity

20072026

most citedSpherical actions on flag varieties

9 citations · 40 across the 21 of their papers we have counts for

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13 papers · 1 filter

math.RT2025

Coadjoint orbits of low dimension for nilradicals of Borel subalgebras in classical types

Mikhail Ignatev, Alexey Petukhov

Let $g$ be a classical simple Lie algebra over an algebraically closed field $F$ of characteristic zero or large enough, and let $n$ be a maximal nilpot…

math.RT2020

The orbit method for locally nilpotent infinite-dimensional Lie algebras

Mikhail V. Ignatyev, Alexey Petukhov

Let $n$ be a locally nilpotent infinite-dimensional Lie algebra over $C$ . Let $U (n)$ and $S (n)$ be its universal envelop…

math.RT2018

Primitive ideals of $U (sl (\infty))$ and the Robinson-Schensted algorithm at infinity

Ivan Penkov, Alexey Petukhov

We present an algorithm which computes the annihilator in $U (sl (\infty))$ of any simple highest weight $sl (\infty)$ -module $L_{b} (λ)$ . This algorithm is bas…

math.RT2017★ 4 cited

Branching rules related to spherical actions on flag varieties

Roman Avdeev, Alexey Petukhov

Let $G$ be a connected semisimple algebraic group and let $H \subset G$ be a connected reductive subgroup. Given a flag variety $X$ of $G$ , a result of Vinberg and Kimelfeld assert…

math.RT2017

On annihilators of bounded $(g, k)$ -modules

Alexey Petukhov

Let $g$ be a semisimple Lie algebra and $k \subset g$ be a reductive subalgebra. We say that a $g$ -module $M$ is a bounded $(g, k)$ -module if $M$ …

math.RT2016

Finite-dimensional representations of minimal nilpotent W-algebras and zigzag algebras

Alexey Petukhov

Let $g$ be a simple finite-dimensional Lie algebra over an algebraically closed field $F$ of characteristic 0. We denote by $U (g)$ the universal…

math.RT2016★ 6 cited

Primitive ideals of $U (sl (\infty))$

Ivan Penkov, Alexey Petukhov

We provide an explicit description of the primitive ideals of the enveloping algebra $U (sl (\infty))$ of the infinite-dimensional finitary Lie algebra $\frak{s…

math.RT2015

On ideals in U $(sl (\infty))$ , U $(o (\infty))$ , U $(sp (\infty))$

Ivan Penkov, Alexey Petukhov

We provide a review of results on two-sided ideals in the enveloping algebra U $(g (\infty))$ of a locally simple Lie algebra $g (\infty)$ . We pay special attention to the…

math.RT2015

On Gelfand-Kirillov conjecture for some W-algebras

Alexey Petukhov

Consider the W-algebra $W$ attached to the smallest nilpotent orbit in a simple Lie algebra $g$ over an algebraically closed field of characteristic 0. We show that if an ana…

math.RT2014★ 1 cited

Annihilators of highest weight $sl (\infty)$ -modules

I. Penkov, A. Petukhov

We give a criterion for the annihilator in U $(sl (\infty))$ of a simple highest weight $sl (\infty)$ -module to be nonzero. As a consequence we show that, in contrast wi…

math.RT2011★ 2 cited

A geometric approach to (g, k)-modules of finite type

Alexey Petukhov

Let $g$ be a semisimple Lie algebra over $C$ and $k$ be a reductive in $g$ subalgebra. We say that a simple $g$ -module $M$ is a $(g; k)$ -module if as a $k$ -module $M$ is a…

math.RT2011

Support varieties of $(g, k)$ -modules of finite type

Alexey V. Petukhov

Let $g$ be a reductive Lie algebra over an algebraically closed field of characteristic 0 and $k$ be a reductive in $g$ -subalgebra. Let $M$ be a finitely generate…

math.RT2010★ 7 cited

Bounded reductive subalgebras of sl(n)

Alexey Petukhov

Let $g$ be a semisimple Lie algebra and $k \subset g$ be a reductive in $g$ subalgebra. A $(g, k)$ -module is a $\mathfrak…

Coadjoint orbits of low dimension for nilradicals of Borel subalgebras in classical types

The orbit method for locally nilpotent infinite-dimensional Lie algebras

Primitive ideals of U(sl(∞)) and the Robinson-Schensted algorithm at infinity

Branching rules related to spherical actions on flag varieties

On annihilators of bounded (g,k)-modules

Finite-dimensional representations of minimal nilpotent W-algebras and zigzag algebras

Primitive ideals of U(sl(∞))

On ideals in U(sl(∞)), U(o(∞)), U(sp(∞))

On Gelfand-Kirillov conjecture for some W-algebras

Annihilators of highest weight sl(∞)-modules

A geometric approach to (g, k)-modules of finite type

Support varieties of (g,k)-modules of finite type

Bounded reductive subalgebras of sl(n)

Primitive ideals of $U (sl (\infty))$ and the Robinson-Schensted algorithm at infinity

On annihilators of bounded $(g, k)$ -modules

Primitive ideals of $U (sl (\infty))$

On ideals in U $(sl (\infty))$ , U $(o (\infty))$ , U $(sp (\infty))$

Annihilators of highest weight $sl (\infty)$ -modules

Support varieties of $(g, k)$ -modules of finite type