Compact Schur-Weyl duality and the Type B/C VW-algebra

In this paper, we study a compact analogue of Schur-Weyl duality for real orthogonal and symplectic groups. We analyse the functors Fμ,k defined in [12], and introduce a new algebra Bkθ. This algebra's finite dimensional modules are naturally a co-domain for the functors Fμ,k. With this new insight, we prove that principle series modules map to principles series modules of graded Hecke algebras and these functors preserve Langlands quotients and unitarity of Harish-Chandra modules.