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Poincaré–Birkhoff–Witt Theorem for Quadratic Algebras of Koszul Type

- A. Braverman, D. Gaitsgory
- Physics, Mathematics
- 16 November 1994

Abstract In this paper we prove a general Poincare–Birkhoff–Witt theorem for quadratic Koszul algebras. The result is similar to that obtained by Polischuk and Positselsky, but the proof is entirely… Expand

Geometric Eisenstein series

- A. Braverman, D. Gaitsgory
- Mathematics
- 12 December 1999

The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence.
Our construction is based on the study of certain relative… Expand

Quantum cohomology of the Springer resolution

- A. Braverman, D. Maulik, A. Okounkov
- Mathematics, Physics
- 31 December 2009

Let G denote a complex, semisimple, simply-connected group. We identify the equivariant quantum differential equation for the cotangent bundle to the flag variety of G with the affine… Expand

Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors

- A. Braverman
- Mathematics, Physics
- 29 January 2004

For a semi-simple simply connected algebraic group G we introduce certain parabolic analogues of the Nekrasov partition function (introduced by Nekrasov and studied recently by Nekrasov-Okounkov and… Expand

Quantum integrable systems and differential Galois theory

- A. Braverman, P. Etingof, D. Gaitsgory
- Mathematics
- 12 July 1996

This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry. We… Expand

Weyl modules and $$q$$q-Whittaker functions

- A. Braverman, M. Finkelberg
- Mathematics
- 7 March 2012

Let $$G$$G be a semi-simple simply connected group over $$\mathbb {C}$$C. Following Gerasimov et al. (Comm Math Phys 294:97–119, 2010) we use the $$q$$q-Toda integrable system obtained by quantum… Expand

Uhlenbeck Spaces via Affine Lie Algebras

- A. Braverman, M. Finkelberg, D. Gaitsgory
- Mathematics
- 2006

Let G be an almost simple simply connected group over ℂ, and let Bun G a (ℙ2, ℙ1) be the moduli scheme of principalG-bundles on the projective plane ℙ2, of second Chern class a, trivialized along a… Expand

Iwahori–Hecke algebras for p-adic loop groups

- A. Braverman, D. Kazhdan, M. Patnaik
- Mathematics
- 3 March 2014

This paper is a continuation of Braverman and Kazhdan (Ann Math (2) 174(3):1603–1642, 2011) in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for… Expand

A Finite Analog of the AGT Relation I: Finite W-Algebras and Quasimaps’ Spaces

- A. Braverman, B. Feigin, M. Finkelberg, L. Rybnikov
- Mathematics, Physics
- 21 August 2010

Recently Alday, Gaiotto and Tachikawa [2] proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This… Expand

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