Dynamical Weyl groups and equivariant cohomology of transversal slices in affine Grassmannians

Details Dynamical Weyl groups and equivariant cohomology of transversal slices in affine Grassmannians Dynamical Weyl groups and equivariant cohomology of transversal slices in affine Grassmannians

2010-10-11

arxiv.org/abs/1010.2135v2

Mathematical Research Letters Volume 18, Issue 3, May 2011 pp. 505-512

Mathematics

Representation Theory

Scientific paper

Let G be a reductive group; in this note we give an interpretation of the dynamical Weyl group of of the Langlands dual group $\check{G}$ defined by Etingof and Varchenko in terms of the geometry of the affine Grassmannian Gr of G. In this interpretation the dynamical parameters of Etingof and Varchenko correspond to equivariant parameters with respect to certain natural torus acting on Gr. We also present a conjectural generalization of our results to the case of affine Kac-Moody groups.

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