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Poincaré–Birkhoff–Witt Theorem for Quadratic Algebras of Koszul Type
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 entirelyExpand
Geometric Eisenstein series
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 relativeExpand
Quantum cohomology of the Springer resolution
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 affineExpand
Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors
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 andExpand
Quantum integrable systems and differential Galois theory
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. WeExpand
Weyl modules and $$q$$q-Whittaker functions
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 quantumExpand
Uhlenbeck Spaces via Affine Lie Algebras
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 aExpand
Iwahori–Hecke algebras for p-adic loop groups
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 forExpand
A Finite Analog of the AGT Relation I: Finite W-Algebras and Quasimaps’ Spaces
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. ThisExpand