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arXiv · 2509.23559

Affine quantum Schur algebras and $\imath$quantum groups with three parameters

Li Luo·Xirui Yu
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Abstract

We study the affine quantum Schur algebras corresponding to the affine Hecke algebras of type C with three parameters. Multiplication formulas for semisimple generators are derived for these algebras. We prove that they admit a stabilization property in the sense of Beilinson-Lusztig-MacPherson, by which we construct quasi-split $\imath$quantum groups of affine type AIII with three parameters. Upon specialization of parameters, we recover some known multiplication formulas for affine quantum Schur algebras of types C and D with equal parameters. We take this opportunity to demonstrate in the appendix that different forms of multiplication formulas for affine quantum Schur algebras of types C with equal parameters across the literature are indeed equivalent.

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Li Luo, Xirui Yu. 2025-09-28. Affine quantum Schur algebras and $\imath$quantum groups with three parameters. https://arxiv.org/abs/2509.23559

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