Howe duality for quantum queer superalgebras

Abstract

We establish a new Howe duality between a pair of quantum queer superalgebras (Uq−1(qn), Uq(qm)). The key ingredient is the construction of a non-commutative analogue Aq(qn,qm) of the symmetric superalgebra S(Cmn|mn) with the use of quantum coordinate queer superalgebra. It turns out that this superalgebra is equipped with a Uq−1(qn)⊗Uq(qm)-supermodule structure that admits a multiplicity-free decomposition. We also show that the (Uq−1(qn),Uq(qm))-Howe duality implies the Sergeev-Olshanski duality.