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 F-mu,F-k defined in [12], and introduce a new algebra B-k(0). This algebra's finite dimensional modules are naturally a co-domain for the functors F-mu,F-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. (C) 2022 The Author(s). Published by Elsevier Inc.