# Howe duality and dynamical Weyl group

Rea Dalipi, Giovanni Felder

Rea Dalipi, Giovanni Felder

**27/8/22**Published in : arXiv:2208.13055

We give a fermionic formula for R-matrices of exterior powers of the vector representations of U_q(\hat{\mathfrak{gl}}_N) and relate it to the dynamical Weyl group of Tarasov-Varchenko and Etingof-Varchenko, via a Howe (\mathfrak{gl}_N,\mathfrak{gl}_M)-duality. As a consequence we obtain a dynamical action of the Weyl group on integrable U_q\mathfrak{gl}_M-modules, extending the known action on zero weight spaces.