Pursuing the double affine Grassmannian I: transversal slices via instantons on A_k-singularities
Preprint
Abstract
This paper is the first in a series that describe a conjectural analog of the geometric Satake isomorphism for an affine Kac-Moody group. In this paper we construct a model for the singularities of some would-be Schubert varieties in the affine Grassmannian for an affine Kac-Moody group. We formulate a conjecture describing the (local) intersection cohomology of these varieties in terms of integrable representations of the Langlands dual affine Kac-Moody group and check this conjecture in a number of cases. Roughly speaking the above singularities are constructed by looking at the Uhlenbeck space of instantons on the quotient of the affine plane by a finite cyclic subgroup of SL(2).Keywords
All Related Versions
This publication has 14 references indexed in Scilit:
- Algebraic loop groups and moduli spaces of bundlesJournal of the European Mathematical Society, 2003
- On quiver varieties and affine Grassmannians of type AComptes Rendus Mathematique, 2003
- Intersection cohomology of Drinfeld‚s compactificationsSelecta Mathematica, 2002
- Kac-Moody Groups, their Flag Varieties and Representation Theory2002
- Geometry of the Moment Map for Representations of QuiversCompositio Mathematica, 2001
- Crystals via the affine GrassmannianDuke Mathematical Journal, 2001
- Sheaves on a loop group and langlands dualityFunctional Analysis and Its Applications, 1990
- Limits of Weight Spaces, Lusztig's q-Analogs, and Fiberings of Adjoint OrbitsJournal of the American Mathematical Society, 1989
- Calculus of twisted vertex operatorsProceedings of the National Academy of Sciences, 1985
- Some Theorems on Actions of Algebraic GroupsAnnals of Mathematics, 1973