Application of Schur-Weyl duality to Springer theory

Abstract

In \cite{FMX19}, it is proved that the convolution algebra of top Borel-Moore homology on Steinberg variety of type $B/C$ realizes $U(s{l}_n^{\theta })$, where $s{l}_n^{\theta }$ is the fixed point subalgebra of involution on $s{l}_n$. So top Borel-Moore homology of the partial Springer's fibers gives the representations of $U(s{l}_n^{\theta })$. In this paper, we study these representations using the Schur-Weyl duality and Springer theory.

9 pages