Mathematical Research Letters

Volume 27 (2020)

Number 1

Quantum Schur duality of affine type C with three parameters

Pages: 79 – 114



Zhaobing Fan (School of Mathematical Sciences, Harbin Engineering University, Harbin, China)

Chun-Ju Lai (Department of Mathematics, University of Georgia, Athens, Ga., U.S.A.)

Yiqiang Li (Department of Mathematics, University at Buffalo, State University of New York, Buffalo, N.Y., U.S.A.)

Li Luo (School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, China)

Weiqiang Wang (Department of Mathematics, University of Virginia, Charlottesville, Va., U.S.A.)

Hideya Watanabe (Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan)


We establish a three-parameter Schur duality between the affine Hecke algebra of type C and a coideal subalgebra of quantum affine $\mathfrak{sl}_n$. At the equal parameter specializations, we obtain Schur dualities of types BCD.

Received 27 March 2018

Accepted 22 April 2019

Published 8 April 2020