相关论文: On cocharacters associated to nilpotent elements o…

We classify the unipotent character sheaves on a fixed connected component of a reductive algebraic group under a mild hypothesis on the characteristic of the ground field.

Let A be a character sheaf on a reductive connected group G over an algebraically closed field. Assuming that the characteristic is not bad, we show that for certain conjugacy classes D in G the restriction of A to D is a local system up to…

Let G be a Lie group over a local field of positive characteristic which admits a contractive automorphism f (i.e., the forward iterates f^n(x) of each group element x converge to the neutral element 1). We show that then G is a torsion…

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

In this paper, we describe the possible disconnected complex reductive algebraic groups $E$ with component group $\Gamma = E/E_0$. We show that there is a natural bijection between such groups $E$ and algebraic extensions of $\Gamma$ by…

Consider a reductive $p$-adic group $G$, its (complex-valued) Hecke algebra $H(G)$ and the Harish-Chandra--Schwartz algebra $S(G)$. We compute the Hochschild homology groups of $H(G)$ and of $S(G)$, and we describe the outcomes in several…

Let $G$ be a reductive algebraic group over an algebraically closed field $k$ of prime characteristic not $2$, whose Lie algebra is denoted $\mathfrak{g}$. We call a subvariety $\mathfrak{X}$ of the nilpotent cone $N \subset \mathfrak{g}$…

Let G be a finite simple group of Lie type. In this paper we study characters of G that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal unipotent subgroup of G. Such characters can be viewed as a…

Let F be an algebraically closed field and let G be a semisimple F-algebraic group for which the characteristic of F is *very good*. If X in Lie(G) = Lie(G)(F) is a nilpotent element in the Lie algebra of G, and if C is the centralizer in G…

Let $G$ be a simply connected algebraic group of type $B,C$ or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the dual vector space of the Lie algebra of $G$. In particular, we…

Graded Hecke algebras can be constructed geometrically, with constructible sheaves and equivariant cohomology. The input consists of a complex reductive group G (possibly disconnected) and a cuspidal local system on a nilpotent orbit for a…

Given a measured space X with commuting actions of two groups G and H satisfying certain conditions, we construct a Hilbert C*(H)-module E(X) equipped with a left action of C*(G), which generalises Rieffel's construction of inducing…

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 $G$ be a connected reductive algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p \ge 0$, and let $\mathcal{N}$ be its nilpotent cone. Under mild hypotheses, we construct for each nilpotent $G$-orbit $C$ and…

Let $\Gamma$ be a finitely generated nilpotent group and let G be a complex reductive algebraic group. The representation variety $\mathrm{Hom}(\Gamma,G)$ and the character variety $\mathrm{Hom}(\Gamma,G)//G$ each carry a natural topology,…

Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $\mathbbm k$ of characteristic zero. We consider the commuting variety $\mathcal C(\mathfrak u)$ of the nilradical $\mathfrak u$ of the Lie algebra…

Parabolic subalgebras $\frak{p}$ of semisimple Lie algebras define a $\Bbb{Z}$-grading of the Lie algebra. If there exists a nilpotent element in the first graded part of $\frak{g}$ on which the adjoint group of $\frak{p}$ acts with a dense…

Let $\mf{g}$ be any finite-dimensional Lie algebra with Killling form $B$. Let $\mf{h}$ be a subalgebra of $\mf{g}$ on which the Killing form is non degenerate. Then $\mf{h}$ is reductive.

For an isotropic reductive group G satisfying a suitable rank condition over an infinite field k, we show that the sections of the $\mathbb{A}^1$-fundamental group sheaf of G over an extension field L/k can be identified with the second…