相关论文: Parametrizing nilpotent orbits via Bruhat-Tits the…

We introduce nil-Hecke algebras for Weyl groupoids. We describe a basis and some properties of these algebras which lead to a notion of Bruhat order for Weyl groupoids.

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 introduce the class of graded Lie-Rinehart algebras as a natural generalization of the one of graded Lie algebras. For $G$ an abelian group, we show that if $L$ is a tight $G$-graded Lie-Rinehart algebra over an associative and…

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…

We prove two results on the defining ideals of certain varieties of matrices. Let us fix two positive integers r, e. Let M(r) be the set of r x r matrices over a field K. We consider the closed subscheme of the nilpotent variety of M(r)…

Let $\mathfrak{g}$ be a simple classical Lie algebra over $\mathbb{C}$ and $G$ be the adjoint group. Consider a nilpotent element $e\in \mathfrak{g}$, and the adjoint orbit $\mathbb{O}=Ge$. The formal slices to the codimension $2$ orbits in…

In Lie theory, a dense orbit in the unipotent radical of a parabolic group under the adjoint action is called a Richardson orbit. We define a quiver-graded version of Richardson orbits generalising the classical definition in the case of…

Let $O$ be a nilpotent orbit of a complex semisimple Lie algebra $\mathfrak{g}$ and let $\pi: X \to \bar{O}$ be the finite covering associated with the universal covering of $O$. In the previous article we have explicitly constructed a…

We define a class of partial orders on a Coxeter group associated with sets of reflections. In special cases, these lie between the left weak order and the Bruhat order. We prove that these posets are graded by the length function and that…

In this paper we consider non-compact non-complex exceptional Lie algebras, and compute the dimensions of the second cohomology groups for most of the nilpotent orbits. For the rest of cases of nilpotent orbits, which are not covered in the…

Given a nilpotent orbit O of a real, reductive algebraic group, a necessary condition is given for the existence of a tempered representation pi such that O occurs in the wave front cycle of pi. The coefficients of the wave front cycle of a…

Let $k$ be a nonperfect separably closed field. Let $G$ be a (possibly non-connected) reductive group defined over $k$. We study rationality problems for Serre's notion of complete reducibility of subgroups of $G$. In our previous work, we…

In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determining the…

Let $G$ be a semisimple algebraic group over the complex numbers and $K$ be a connected reductive group mapping to $G$ so that the Lie algebra of $K$ gets identified with a symmetric subalgebra of $\mathfrak{g}$. So we can talk about…

In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on a generalized Verma module to quantize the Kirillov bracket…

Let $G$ be a real reductive Lie group and ${\tau}:G \longrightarrow GL(V)$ be a real reductive representation of $G$ with (restricted) moment map $m_{\ggo}: V-{0} \longrightarrow \ggo$. In this work, we introduce the notion of "nice space"…

Let $G$ be a simple algebraic group and $\ggg=\Lie(G)$ over $k=\bar\bbf_q$ where $q$ is a power of the prime characteristic of $k$, and $F$ a Frobenius morphism on $G$ which can be defined naturally on $\ggg$. In this paper, we investigate…

Motivated by geometric Langlands, we initiate a program to study the mirror symmetry between nilpotent orbit closures of a semisimple Lie algebra and those of its Langlands dual. The most interesting case is $B_n$ via $C_n$. Classically,…

For an essentially tame supercuspidal representation $\pi$ of a connected reductive $p$-adic group $G$, we establish two distinct and complementary sufficient conditions for the irreducible components of its restriction to a maximal compact…

We study certain spaces of nilpotent orbits in Hodge domains, and treat a number of examples. More precisely, we compute the Mumford-Tate group of the limit mixed Hodge structure of a generic such orbit. The result is used to present these…