Speaker
Description
Howe duality, which will be reviewed in this talk, is a gl_M-gl_N
duality generalizing the Schur-Weyl duality. It also has a quantum
group version. We give a fermionic formula for R-matrices for exterior
powers of vector representations of the quantum loop algebra U_q(Lgl_N)
based on Howe duality. The formula is suitable for taking the large N
limit and obtaining the R-matrix for Fock spaces. In the Yangian limit
we recover a version of a formula proposed by A. Smirnov for instanton
R-matrices. The duality relates R-matrices to the dynamical Weyl group
of Etingof, Tarasov and Varchenko. One of the consequences is a
dynamical action of the dynamical 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.
