## 7 Citations

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

- MathematicsSelecta Mathematica
- 2018

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

- MathematicsAlgebraic Geometry: Salt Lake City 2015
- 2018

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

- MathematicsProceedings 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

- Mathematics
- 2018

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

- MathematicsSelecta Mathematica
- 2018

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

- Computer ScienceRepresentation Theory of the American Mathematical Society
- 2022

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.

- Mathematics
- 2020

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…

## References

SHOWING 1-10 OF 51 REFERENCES

### Principal G bundles over elliptic curves

- Mathematics
- 1997

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

- Mathematics
- 2005

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

- Mathematics
- 2012

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

- Mathematics
- 2009

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

- Mathematics
- 2012

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

- MathematicsCompositio Mathematica
- 2010

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 $\mathbb{A}^2$

- Mathematics
- 2009

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

- Mathematics
- 1957

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

- Mathematics
- 2000

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…