Related papers: Richardson elements for classical Lie algebras

We study the Delta-filtered modules for the Auslander algebra of k[T]/T^n\rtimes C_2 where C_2 is the cyclic group of order two. The motivation for this is the bijection between parabolic orbits in the nilradical of a parabolic subgroup of…

Given a hyperplane arrangement in a complex vector space of dimension n, there is a natural associated arrangement of codimension k subspaces in a complex vector space of dimension k*n. Topological invariants of the complement of this…

A new highly symmetrical model of the compact Lie algebra $\mathfrak{g}^c_2$ is provided as a twisted ring group for the group $\mathbb{Z}_2^3$ and the ring $\mathbb{R}\oplus\mathbb{R}$. The model is self-contained and can be used without…

In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous papers. On the basis of new classification of Clifford algebra elements it is possible to find out…

We consider a system with symmetries whose configuration space is a compact Lie group, acted upon by inner automorphisms. The classical reduced phase space of this system decomposes into connected components of orbit type subsets. To…

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.…

Let $G$ be an adjoint algebraic group of type $B$, $C$, or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of $G$. In particular, for orthogonal Lie algebras in…

Following the structure theory approach for rings, the aim of this paper is to study some distinguished classes of Lie algebras. We introduce the notion of a Lie-module and discuss some relations of it with various classes of ideals of a…

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over $\tF_{2^n}$. Let $G$ be an adjoint algebraic group of type $B,C$ or $D$ defined over an algebraically closed field…

Let $\mathfrak{n}$ be a locally nilpotent infinite-dimensional Lie algebra over $\mathbb{C}$. Let $\mathrm{U}(\mathfrak{n})$ and $\mathrm{S}(\mathfrak{n})$ be its universal enveloping algebra and its symmetric algebra respectively. Consider…

We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Mili\v{c}i\'c-Soergel equivalence of a category of Whittaker modules and a category of Harish-Chandra…

We investigate the properties of principal elements of Frobenius Lie algebras, following the work of M. Gerstenhaber and A. Giaquinto. We prove that any Lie algebra with a left symmetric algebra structure can be embedded, in a natural way,…

Every real simple non-compact Lie algebra not isomorphic to $\mathfrak{so}(1,n)$ contains a unique standard parabolic subalgebra whose nilradical is a generalized Heisenberg algebra. Here we discuss the associated parabolic geometries and…

Classical mechanical systems are defined by their kinetic and potential energies. They generate a Lie algebra under the canonical Poisson bracket. This Lie algebra, which is usually infinite dimensional, is useful in analyzing the system,…

In the first part of this paper, we discuss the classical W-algebra $\mathcal{W}(\mathfrak{g}, F)$ associated with a Lie superalgebra $\mathfrak{g}$ and the nilpotent element $F$ in an $\mathfrak{sl}_2$-triple. We find a generating set of…

Let $G$ be a classical group with natural module $V$ and Lie algebra $\mathfrak{g}$ over an algebraically closed field $K$ of good characteristic. For rational irreducible representations $f: G \rightarrow \operatorname{GL}(W)$ occurring as…

Let $\mathcal{O}$ be a Richardson nilpotent orbit in a simple Lie algebra $\mathfrak{g}$ over $\mathbb C$, induced from a Levi subalgebra whose simple roots are orthogonal short roots. The main result of the paper is a description of a…

We characterize locally semisimple subalgebras $\l$ of $\sl_\infty$, $\so_\infty$, and $\sp_\infty$ which are Levi components of parabolic subalgebras. Given $\l$, we characterize the parabolic subalgebras $\p$ such that $\l$ is a Levi…

In this note, we initiate the systematic study of the Lie algebra structure of the necklace Lie algebra n of a free algebra in 2d variables. We begin by giving a description of n as an sp(2d)-module. Specializing to d = 1, we decompose n…

Let $\g$ be a locally reductive complex Lie algebra which admits a faithful countable-dimensional finitary representation $V$. Such a Lie algebra is a split extension of an abelian Lie algebra by a direct sum of copies of $\sl_\infty$,…