BRAID GROUP ACTION AND QUASI-SPLIT AFFINE iQUANTUM GROUPS I

被引：2

作者：

Lu, Ming ^{[1
]}

Wang, Weiqiang ^{[2
]}

Zhang, Weinan ^{[2
]}

机构：

[1] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China

[2] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

来源：

REPRESENTATION THEORY | 2023年 / 27卷

基金：

中国国家自然科学基金;

关键词：

Affine iquantum groups; braid group action; quantum symmetric pairs; Drinfeld presentation; QUANTUM; ALGEBRA;

D O I：

10.1090/ert/657

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This is the first of our papers on quasi-split affine quantum symmetric pairs (U) over tilde ((g) over cap), (U) over tilde (i), focusing on the real rank one case, i.e., g = sl(3) equipped with a diagram involution. We construct explicitly a relative braid group action of type A(2)((2)) on the affine iquantum group (U) over tilde (i). Real and imaginary root vectors for (U) over tilde (i) are constructed, and a Drinfeld type presentation of (U) over tilde (i) is then established. This provides a new basic ingredient for the Drinfeld type presentation of higher rank quasi-split affine iquantum groups in the sequels.

引用

页码：1000 / 1040

页数：41

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