Howe duality for quantum queer superalgebras

Authors：Chang, Zhihua; Wang, Yongjie^*

Source：Journal of Algebra, 2020, 547: 358-378.

DOI：10.1016/j.jalgebra.2019.11.023

• Quantum queer superalgebra
• Sergeev-Olshanski duality
• Howe duality

We establish a new Howe duality between a pair of quantum queer superalgebras (Uq-1(q(n)), U-q(q(m))). The key ingredient is the construction of a non-commutative analogue A(q)(q(n), q(m)) of the symmetric superalgebra S(C-mn vertical bar mn) with the use of quantum coordinate queer superalgebra. It turns out that this superalgebra is equipped with a Uq-1(q(n))circle times U-q(q(m))-supermodule structure that admits a multiplicity-free decomposition. We also show that the (Uq-1(q(n)), U-q(q(m)))-Howe duality implies the Sergeev-Olshanski duality.