Related papers: Quasi-admissible, raisable nilpotent orbits and co…

We study the quasi-admissibility and raisablility of some nilpotent orbits of a covering group. In particular, we determine the degree of the cover such that a given split nilpotent orbit is quasi-admissible and non-raisable. The speculated…

We propose a systematic and topological study of limits $\lim_{\nu\to 0^+}G_\mathbb{R}\cdot(\nu x)$ of continuous families of adjoint orbits for non-compact simple Lie groups. This limit is always a finite union of nilpotent orbits. We…

Let G be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit O through a…

Let $F$ be either $\mathbb{R}$ or a finite extension of $\mathbb{Q}_p$, and let $G$ be a finite central extension of the group of $F$-points of a reductive group defined over $F$. Also let $\pi$ be a smooth representation of $G$ (Frechet of…

Let $G$ be a classical linear algebraic group over an algebraically closed field, and let $\mathfrak{n}$ denote the subset of nilpotent elements in its Lie algebra. In this paper we study a partial order on the $G$-orbits in $\mathfrak{n}$…

Let $G$ be a semisimple algebraic group with Lie algebra $\mathfrak g$. For a nilpotent $G$-orbit $\mathcal O\subset\mathfrak g$, let $d_\mathcal O$ denote the maximal dimension of a subspace $V\subset \mathfrak g$ that is contained in the…

In analogy with the Barbasch-Vogan duality for real reductive linear groups, we introduce a duality notion useful for the representation theory of the real metaplectic groups. This is a map on the set of nilpotent orbits in a complex…

Let $G$ be a simple simply-connected algebraic group over an algebraically closed field $k$ of characteristic $p>0$ with $\mathfrak{g}={\rm Lie}(G)$. We discuss various properties of nilpotent orbits in $\mathfrak{g}$, which have previously…

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra of type A of admissible level k. For admissible simple highest weight modules corresponding to the…

Let $G$ be a complex reductive algebraic group. In arXiv:2108.03453, we have defined a finite set of irreducible admissible representations of $G$ called `unipotent representations', generalizing the special unipotent representations of…

Let $G$ be a non-compact classical semisimple Lie group and let $G/V$ be the adjoint orbit with respect to a fixed element in $G$. These manifolds can be equipped with an almost-K\"ahler structure and we provide explicit formulae for the…

We obtain a Lie theoretic intrinsic characterization of the connected and simply connected solvable Lie groups whose regular representation is a factor representation. When this is the case, the corresponding von Neumann algebras are…

A contact structure on a complex manifold M is a corank 1 subbundle F of T(M) such that the bilinear form on F with values in the quotient line bundle L=T(M)/F deduced from the Lie bracket of vector fields is everywhere non-degenerate. In…

Let X be an F-rational nilpotent element in the Lie algebra of a connected and reductive group G defined over the ground field F. Suppose that the Lie algebra has a non-degenerate invariant bilinear form. We show that the unipotent radical…

Let $\0$ be a nilpotent orbit in a semisimple complex Lie algebra $\g$. Denote by $G$ the simply connected Lie group with Lie algebra $\g$. For a $G$-homogeneous covering $M \to \0$, let $X$ be the normalization of $\bar{\0}$ in the…

In this paper, we investigate nilpotent and unimodular solvable Lie groups that admit quasi-Einstein metrics $(M,g,X)$ with $X$ a left-invariant vector field, which we call totally left-invariant quasi-Einstein metrics. We give a complete…

The orbital varieties are the irreducible components of the intersection between a nilpotent orbit and a Borel subalgebra of the Lie algebra of a reductive group. There is a geometric correspondence between orbital varieties and irreducible…

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…

We give a simple description of the closure of the nilpotent orbits appearing as associated varieties of admissible affine vertex algebras in terms of primitive ideals.

We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra $\mathfrak{g}$ and those in its complexification $\mathfrak{g}_{\mathbb{C}}$. In particular, we prove that two distinct real nilpotent orbits…