Howe Duality for Quantum Queer Superalgebras

2018/05/13 by Chang, Zhihua, Wang, Yongjie
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1805.04809

Abstract

We establish a new Howe duality between a pair of quantum queer superalgebras (U_q^-1(\mathfrakq_n), U_q(\mathfrakq_m)). The key ingredient is the construction of a non-commutative analogue A_q(\mathfrakq_n,\mathfrakq_m) of the symmetric superalgebra S(ℂ^mn|mn) with the use of quantum coordinate queer superalgebra. It turns out that this superalgebra is equipped with a U_q^-1(\mathfrakq_n)\otimesU_q(\mathfrakq_m)-supermodule structure that admits a multiplicity-free decomposition. We also show that the (U_q^-1(\mathfrakq_n),U_q(\mathfrakq_m))-Howe duality implies the Sergeev-Olshanski duality.

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