The i-Quantum Group U^ (n), II: Presenting their q-Schur Algebras

Abstract Since the establishment of the quantum Schur–Weyl duality in Jimbo (Lett. Math. Phys. 11, 247–252, 1986), the duality pair (U (glₙ), H (Sᵣ) ) (U (gl n), H (S r) ) of type A has been extended to the duality pairs (U^ (n), H (Bᵣ) ) (U ȷ (n), H (B r) ) and (U^ (n), H (Cᵣ) ) (U ı (n), H (C r) ) in the Hecke algebra series in Bao and Wang (Astérisque 402, vii+134, 2018), where U^ (n), U^ (n) U ȷ (n), U ı (n) are i -quantum groups arising from certain quantum symmetric pairs. The quantum Schur algebra associated with the pair (U (glₙ), H (Sᵣ) ) (U (gl n), H (S r) ) has a nice and simple presentation; see Doty and Giaquinto (2002). In this paper, we tackle the presentation problem for the i -quantum Schur algebras associated with the duality pair (U^ (n), H (Cᵣ) ) (U ı (n), H (C r) ). Suc