%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 }