"We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and canonical bases for the affine Schur algebra. The multiplication formula allows us to establish a stabilization property of the family of affine Schur algebras that leads to the modified version of an algebra Kc n. We show that Kc n is a coideal subalgebra of quantum affine algebra Uppglnq, and Uppglnq,Kc nq forms a quantum symmetric pair. The modified coideal subalgebra is shown to admit monomial and stably canonical bases. We also formulate several variants of the affine Schur algebra and the (modified) coideal subalgebra above, as well as their monomial and canonical bases. This work provides a new and algebraic approach which complements and sheds new light on our previous geometric approach on the subject. In the appendix by four of the authors, new length formulas for the Weyl groups of affine classical types are obtained in a symmetrized fashion"--
Introducing an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C, Fan and colleagues establish multiplication formulas on the affine Hecke algebra and affine Schur algebra, then construct monomial bases and canonical bases for the affine Schur algebra. This work provides a new and algebraic approach to affine Schur algebra that complements and sheds new light on their previous geometric approach to the subject. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
Zhaobing Fan, Harbin Engineering University, China.
Chun-Ju Lai, Institute of Mathematics, Academia Sinica, Taipei, Taiwan.
Yiqiang Li, SUNY at Buffalo, New York.
Li Luo, East China Normal University, Shanghai, China.
Weiqiang Wang, University of Virginia, Charlottesville, Virginia.
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