Uniformization of semistable bundles on elliptic curves

  title={Uniformization of semistable bundles on elliptic curves},
  author={Penghui Li and David Nadler},
  journal={arXiv: Representation Theory},

Generalized Springer theory for D-modules on a reductive Lie algebra

Given a reductive group G, we give a description of the abelian category of G-equivariant D-modules on $$\mathfrak {g}={{\mathrm{Lie}}}(G)$$g=Lie(G), which specializes to Lusztig’s generalized

Betti Geometric Langlands

We introduce and survey a Betti form of the geometric Langlands conjecture, parallel to the de Rham form developed by Beilinson-Drinfeld and Arinkin-Gaitsgory, and the Dolbeault form of

A colimit of traces of reflection groups

  • Penghui Li
  • Mathematics
    Proceedings of the American Mathematical Society
  • 2019
Li-Nadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti geometric Langlands conjecture of Ben-Zvi-Nadler in genus 1. We prove a Weyl group

Derived categories of character sheaves

We give a block decomposition of the dg category of character sheaves on a simple and simply-connected complex reductive group $G$, similar to the one in generalized Springer correspondence. As a

Generalized Springer theory for D-modules on a reductive Lie algebra

Given a reductive group G, we give a description of the abelian category of G-equivariant D-modules on g=Lie(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}

The Jordan–Chevalley decomposition for 𝐺-bundles on elliptic curves

The moduli stack of degree of degree is a connected reductive group in arbitrary characteristic and a partition of this stack indexed by a certain family ofconnected reductive subgroups is described.

A microlocal criterion for commuting nearby cycles.

We present a microlocal criterion for the equivalence of iterated nearby cycles along different flags of subspaces in a higher-dimensional base. We also sketch an intended application to Hitchin



Principal G bundles over elliptic curves

Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof

On the Hall algebra of an elliptic curve, I

This paper is a sequel to math.AG/0505148, where the Hall algebra U^+_E of the category of coherent sheaves on an elliptic curve E defined over a finite field was explicitly described, and shown to

Isospectral commuting variety, the Harish-Chandra $\mathbf{\mathcal{D}}$-module, and principal nilpotent pairs

Let g be a complex reductive Lie algebra with Cartan algebra h. Hotta and Kashiwara defined a holonomic D-module M, on g x h, called Harish-Chandra module. We relate gr(M), an associated graded

The Character Theory of a Complex Group

We apply the ideas of derived algebraic geometry and topological field theory to the representation theory of reductive groups. Our focus is the Hecke category of Borel-equivariant D-modules on the

On two geometric realizations of an affine Hecke algebra

The article is a contribution to the local theory of geometric Langlands duality. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra associated to a

The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials

Abstract We exhibit a strong link between the Hall algebra HX of an elliptic curve X defined over a finite field 𝔽l (or, more precisely, its spherical subalgebra U+X) and Cherednik’s double affine

The elliptic Hall algebra and the equivariant K-theory of the Hilbert scheme of $\mathbb{A}^2$

In this paper we compute the convolution algebra in the equivariant K-theory of the Hilbert scheme of A^2. We show that it is isomorphic to the elliptic Hall algebra, and hence to the spherical DAHA

Vector Bundles Over an Elliptic Curve

Introduction THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve lies

Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction

This paper continues the study of holomorphic semistable principal G-bundles over an elliptic curve. In this paper, the moduli space of all such bundles is constructed by considering deformations of