• Corpus ID: 18205637

The Character Theory of a Complex Group

  title={The Character Theory of a Complex Group},
  author={David Ben-Zvi and David Nadler},
  journal={arXiv: Representation Theory},
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 flag variety of a complex reductive group G (equivalently, the category of Harish Chandra bimodules of trivial central character) and its monodromic variant. The Hecke category is a categorified analogue of the finite Hecke algebra, which is a finite-dimensional semi-simple symmetric Frobenius… 

Nonlinear Traces

We combine the theory of traces in homotopical algebra with sheaf theory in derived algebraic geometry to deduce general fixed point and character formulas. The formalism of dimension (or Hochschild

Integral Transforms and Opers in the Geometrical Langlands Program

6  Abstract— A problem in derived geometry is determine the cycles and co-cycles that can conform the Langlands correspondence via the Penrose transforms on generalized D-modules in moduli stacks

Integrating quantum groups over surfaces: quantum character varieties and topological field theory

Braided tensor categories give rise to (partially defined) extended 4-dimensional topological field theories, introduced in the modular case by Crane-Yetter-Kauffman. Starting from modules for the

Penrose Transform on Induced DG/H-Modules and Their Moduli Stacks in the Field Theory

We consider generalizations of the Radon-Schmid transform on coherent DG/H-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects

Explorer Integrating quantum groups over surfaces

We apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the (0, 1,

Character D-modules via

The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of HarishChandra bimodules is related to convolution of

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

Towards a functor between affine and finite Hecke categories in type A

In this thesis we construct a functor from the perfect subcategory of the coherent version of the affine Hecke category in type A to the finite constructible Hecke category, partly categorifying a

Truncated convolution of character sheaves

Let G be a reductive connected group over an algebraic closure of a finite field. I define a tensor structure on the category of perverse sheaves on G which are direct sums of unipotent character


For a reductive group $G$ over a finite field, we show that the neutral block of its mixed Hecke category with a fixed monodromy under the torus action is monoidally equivalent to the mixed Hecke



Loop Spaces and Langlands Parameters

We apply the technique of S^1-equivariant localization to sheaves on loop spaces in derived algebraic geometry, and obtain a fundamental link between two families of categories at the heart of

Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I

We develop geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. Geometric approach clarifies several

Equivariant cohomology, Koszul duality, and the localization theorem

(1.1) This paper concerns three aspects of the action of a compact group K on a space X . The ®rst is concrete and the others are rather abstract. (1) Equivariantly formal spaces. These have the

The Classification of Two-Dimensional Extended Topological Field Theories

We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby we classify these

Koszul Duality Patterns in Representation Theory

The aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of Koszul duality to repre- sentation theory. The paper consists of three parts

Integral Transforms and Drinfeld Centers in Derived Algebraic Geometry

We study the interaction between geometric operations on stacks and algebraic operations on their categories of sheaves. We work in the general setting of derived algebraic geometry: our basic

Character D-modules via Drinfeld center of Harish-Chandra bimodules

The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of Harish-Chandra bimodules is related to convolution

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is to study the homotopy theory of dg-categories up to quasi-equivalences. Our main result is a description of the mapping spaces between two dg-categories C and D in