Howe duality and dynamical Weyl group (Giovanni Felder)Colloquium
Orateur : Giovanni Felder (ETHZ)
The symmetric group plays two different roles in the representation theory of the general linear groups: as the Weyl group and as the automorphism group of permutations of factors in tensor powers of representations. R-matrices of affine quantum groups give a version of the latter "with (spectral) parameters". Also the Weyl group has a version with parameters, the dynamical Weyl group of Etingof, Tarasov and Varchenko. We show that the two are related by Howe duality, a generalization of Schur-Weyl duality that will be reviewed in this talk. As a consequence we give a dynamical action of the Weyl group on integrable U_q(gl_M)-modules extending the known action on zero weight spaces. The talk is based on joint work with Rea Dalipi.