A type C study of Braverman-Gaitsgory-Ginzburg's construction of sln representations

In [FMX19], it is proved that the convolution algebra of top Borel-Moore homology on Steinberg variety of type B/C realizes U (sl n θ ) where sl n θ is the fixed point subalgebra of involution on sl n . So top Borel-Moore homology of the partial Springer’s fibers gives the representations of U (sl n θ ) . In this paper, we study these representations using the Schur-Weyl duality and Springer theory.