0. Introduction 0.1. Homogeneous quadratic algebras. Let V be a vector space over some field k and let T (V) = âŠ• T i be its tensor algebra over k. Fix a subspace R âŠ‚ T 2 = V âŠ— V , consider theâ€¦ (More)

Let G be an almost simple simply connected group over C, and let Bun a G (P 2 , P 1) be the moduli scheme of principal G-bundles on the projective plave P 2 , of second Chern class a, trivializedâ€¦ (More)

Let G be a simple simply connected algebraic group over C with Lie algebra g. Given a parabolic subgroup P âŠ‚ G, in [1] the first author introduced a certain generating function Z aff G,P. Roughlyâ€¦ (More)

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. Weâ€¦ (More)

Let g be a simple complex Lie algebra, G the corresponding simply connected group; let also gaff be the corresponding untwisted affine Lie algebra. For a parabolic subgroup P âŠ‚ G we introduce aâ€¦ (More)

Let G be a connected reductive group over C, and let gâˆ¨ be the Langlands dual Lie algebra. Crystals for gâˆ¨ are combinatorial objects that were introduced by M. Kashiwara (cf., e.g., [6]) as certainâ€¦ (More)

This is the second paper of a series (started by [3]) which describes a conjec-tural analog of the affine Grassmannian for affine Kac-Moody groups (also known as the double affine Grassmannian). Theâ€¦ (More)

Let X be a smooth projective algebraic curve of genus > 1 over and algebraically closed field k of characteristic p > 0. Denote by Bunn (resp. Locn) the moduli stack of vector bundles of rank n on Xâ€¦ (More)

Let G be the group of points of a split reductive algebraic group G over a local field k and let X = G/U where U is the group of k-points of a maximal unipotent subgroup of G. In this paper weâ€¦ (More)

We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalization of the Satake isomor-phism for these algebras, relatingâ€¦ (More)