Mathematical Research Letters

Volume 18 (2011)

Number 3

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

Pages: 505 – 512



Alexander Braverman (Brown University, 151 Thayer St., Providence RI 02912, USA)

Michael Finkelberg (IMU, IITP and State University Higher School of Economics, Department of Mathematics, 20 Myasnitskaya st, Moscow 101000 Russia)


Let $G$ be a reductive group and let $\check{G}$ be its Langlands dual. We give an interpretation of the dynamical Weyl group of $\check{G}$ defined in \cite{EV} in terms of the geometry of the affine Grassmannian $\Gr$ of $G$. In this interpretation the dynamical parameters of \cite{EV} 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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