Zobrazeno 1 - 10
of 264
pro vyhledávání: '"Panyushev, Dmitri"'
Autor:
Panyushev, Dmitri I.
Let $G$ be a simple algebraic group with $\mathfrak g=Lie(G)$ and $\mathcal O\subset\mathfrak g$ a nilpotent orbit. If $H$ is a reductive subgroup of $G$ with $Lie(H)=\mathfrak h$, then $\mathfrak g=\mathfrak h\oplus\mathfrak m$, where $\mathfrak m=\
Externí odkaz:
http://arxiv.org/abs/2410.09876
Autor:
Panyushev, Dmitri I.
For a subgroup $H$ of a reductive group $G$, let $\mathfrak m\subset \mathfrak g^*$ be the cotangent space of $eH\in G/H$. The linear action $(H:\mathfrak m)$ is the coisotropy representation. It is known that the complexity and rank of $G/H$ (denote
Externí odkaz:
http://arxiv.org/abs/2405.01897
Autor:
Panyushev, Dmitri I.
Let $\mathfrak g$ be a complex simple Lie algebra and $\mathfrak n$ the nilradical of a parabolic subalgebra of $\mathfrak g$. We consider some properties of the coadjoint representation of $\mathfrak n$ and related algebras of invariants. This inclu
Externí odkaz:
http://arxiv.org/abs/2310.18945
Autor:
Panyushev, Dmitri, Yakimova, Oksana
Let $\mathfrak g$ be a semisimple Lie algebra, $\vartheta\in {\sf Aut}(\mathfrak g)$ a finite order automorphism, and $\mathfrak g_0$ the subalgebra of fixed points of $\vartheta$. Recently, we noticed that using $\vartheta$ one can construct a penci
Externí odkaz:
http://arxiv.org/abs/2211.10664
Autor:
Panyushev, Dmitri I.
Let $\mathfrak g$ be a complex simple Lie algebra and $\mathfrak b=\mathfrak t\oplus\mathfrak u^+$ a fixed Borel subalgebra. Let $\Delta^+$ be the set of positive roots associated with $\mathfrak u^+$ and $\mathcal K\subset\Delta^+$ the Kostant casca
Externí odkaz:
http://arxiv.org/abs/2205.09994
Autor:
Panyushev, Dmitri I.
Let $\mathfrak g$ be a complex simple Lie algebra. We classify the parabolic subalgebras $\mathfrak p$ of $\mathfrak g$ such that the nilradical of $\mathfrak p$ has a commutative polarisation. The answer is given in terms of the Kostant cascade. It
Externí odkaz:
http://arxiv.org/abs/2108.07750
Autor:
Panyushev, Dmitri I.
Let $G$ be a simple algebraic group with $\mathfrak g=\mathsf{Lie} G$ and $\mathcal O_{\sf min}\subset\mathfrak g$ the minimal nilpotent orbit. For a $\mathbb Z_2$-grading $\mathfrak g=\mathfrak g_0\oplus\mathfrak g_1$, let $G_0$ be a connected subgr
Externí odkaz:
http://arxiv.org/abs/2105.02709
Let $\mathfrak g$ be a finite-dimensional Lie algebra. The symmetric algebra $\mathcal S(\mathfrak g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates the second
Externí odkaz:
http://arxiv.org/abs/2102.10065
Autor:
Panyushev, Dmitri I.
Let $\sigma$ be an involution of a complex semisimple Lie algebra $\mathfrak g$ and $\mathfrak g=\mathfrak g_0\oplus\mathfrak g_1$ the related $\mathbb Z_2$-grading. We study relations between nilpotent $G_0$-orbits in $\mathfrak g_0$ and the respect
Externí odkaz:
http://arxiv.org/abs/2101.09228
Let $\mathfrak g$ be a semisimple Lie algebra, $\mathfrak h\subset\mathfrak g$ a reductive subalgebra such that $\mathfrak h^\perp$ is a complementary $\mathfrak h$-submodule of $\mathfrak g$. In 1983, Bogoyavlenski claimed that one obtains a Poisson
Externí odkaz:
http://arxiv.org/abs/2012.04014