Braid group actions for quantum symmetric pairs of type AIII/AIV

被引：9

作者：

Dobson, Liam ^{[1
]}

机构：

[1] Newcastle Univ, Sch Math Stat & Phys, Herschel Bldg, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

来源：

JOURNAL OF ALGEBRA | 2020年 / 564卷

关键词：

Quantum groups; Quantum symmetric pairs; Braid groups; COIDEAL SUBALGEBRAS;

D O I：

10.1016/j.jalgebra.2020.05.038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper we construct braid group actions on quantum symmetric pair coideal subalgebras of type AIII/AIV. This completes the proof of a conjecture by Kolb and Pellegrini in the case where the underlying Lie algebra is sln. The braid group actions are defined on the generators of the coideal subalgebras and the defining relations and braid relations are verified by explicit calculations. Crown Copyright (C) 2020 Published by Elsevier Inc. All rights reserved.

引用

页码：151 / 198

页数：48

共 50 条

[1] Quantum supersymmetric pairs and ıSchur duality of type AIII
Shen, Yaolong
JOURNAL OF ALGEBRA, 2025, 661 : 853 - 903
[2] BRAID GROUP ACTIONS, BAXTER POLYNOMIALS, AND AFFINE QUANTUM GROUPS
Friesen, Noah
Weekes, Alex
Wendlandt, Curtis
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2025, 378 (02) : 1329 - 1372
[3] Braid group actions of quantum Borcherds-Bozec algebras
Fan, Zhaobing
Tong, Bolun
JOURNAL OF ALGEBRA, 2023, 621 : 92 - 115
[4] BRAID GROUP ACTIONS FROM CATEGORICAL SYMMETRIC HOWE DUALITY ON DEFORMED WEBSTER ALGEBRAS
M. KHOVANOV
A. D. LAUDA
J. SUSSAN
Y. YONEZAWA
Transformation Groups, 2022, 27 : 919 - 982
[5] BRAID GROUP ACTIONS FROM CATEGORICAL SYMMETRIC HOWE DUALITY ON DEFORMED WEBSTER ALGEBRAS
Khovanov, M.
Lauda, A. D.
Sussan, J.
Yonezawa, Y.
TRANSFORMATION GROUPS, 2022, 27 (03) : 919 - 982
[6] Finite orbits of the braid group actions
Zhang, Jialin
JOURNAL OF GEOMETRY AND PHYSICS, 2025, 207
[7] Braid group actions and tensor products
Chari, V
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2002, 2002 (07) : 357 - 382
[8] Braid actions on quantum toroidal superalgebras
Bezerra, Luan
Mukhin, Evgeny
JOURNAL OF ALGEBRA, 2021, 585 : 338 - 369
[9] GLOBAL CRYSTAL BASES FOR INTEGRABLE MODULES OVER A QUANTUM SYMMETRIC PAIR OF TYPE AIII
Watanabe, Hideya
REPRESENTATION THEORY, 2021, 25 : 27 - 66
[10] Type D Fock Spaces and Quantum Symmetric Pairs
Ehrig M.
Gan K.
Beijing Ligong Daxue Xuebao/Transaction of Beijing Institute of Technology, 2023, 43 (08): : 878 - 884

← 1 2 3 4 5 →