Schur Algebras and Quantum Symmetric Pairs With Unequal Parameters
Schur Algebras and Quantum Symmetric Pairs With Unequal Parameters
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Schur 代数和具有不等参数的量子对称对
DOI：
10.1093/imrn/rnz110
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发表时间：
--
影响因子：
1
通讯作者：
Li Luo
中科院分区：
文献类型：
--
作者：
Chun-Ju Lai;Li Luo
研究了具有不等参数的Hecke代数对应的B/C型(量子)Schur代数。我们证明了Schur代数提供了Beilinson-Lusztig-MacPherson意义下的稳定化结构，它构造了AIII/AIV型量子对称对上理想子代数的多参数升级.进一步得到了Schur/上理想子代数在任意权函数下的典范基。这些基是具有不等参数的Hecke代数的Lusztig不变基的对应。在附录中，我们给出了D型Beilinson-Lusztig-MacPherson结构的代数形式，这是由Fan-Li首先从几何观点引入的。
We study the (quantum) Schur algebras of type B/C corresponding to the Hecke algebras with unequal parameters. We prove that the Schur algebras afford a stabilization construction in the sense of Beilinson–Lusztig–MacPherson that constructs a multiparameter upgrade of the quantum symmetric pair coideal subalgebras of type AIII/AIV with no black nodes. We further obtain the canonical basis of the Schur/coideal subalgebras, at the specialization associated with any weight function. These bases are the counterparts of Lusztig’s bar-invariant basis for Hecke algebras with unequal parameters. In the appendix we provide an algebraic version of a type D Beilinson–Lusztig–MacPherson construction, which is first introduced by Fan–Li from a geometric viewpoint.