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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 entirely
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 relative
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 and
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. We
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 for
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 quantum
Instanton counting via affine Lie algebras II: From Whittaker vectors to the Seiberg-Witten prepotential
Let G be a simple simply connected algebraic group over ℂ with Lie algebra \( \mathfrak{g} \) . Given a parabolic subgroup P ⊂ G, in tikya[1] the first author introduced a certain generating function
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. This