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).
%0 Journal Article
%1 braverman_pursuingdouble_2007
%A Braverman, Alexander
%A Finkelberg, Michael
%D 2007
%J 0711.2083
%K imported
%T Pursuing the double affine Grassmannian I: transversal slices via instantons on A\_k-singularities
%U http://arxiv.org/abs/0711.2083
%X 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).
@article{braverman_pursuingdouble_2007,
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).}},
added-at = {2009-05-11T21:36:02.000+0200},
author = {Braverman, Alexander and Finkelberg, Michael},
biburl = {https://www.bibsonomy.org/bibtex/2413679b5d9b5c21635402af685b40f41/tbraden},
interhash = {edc9e115d7b3777a6b304ddce76300a3},
intrahash = {413679b5d9b5c21635402af685b40f41},
journal = {0711.2083},
keywords = {imported},
month = {November},
timestamp = {2009-05-11T21:36:02.000+0200},
title = {Pursuing the double affine Grassmannian I: transversal slices via instantons on A\_k-singularities},
url = {http://arxiv.org/abs/0711.2083},
year = 2007
}