Differential operator realization of braid group action on ıquantum groups (2024)

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Volume 64, Issue 10

October 2023

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Research Article| October 16 2023

Zhaobing Fan

;

Zhaobing Fan a)

(Writing – original draft)

Harbin Engineering University

, Harbin,

China

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Jicheng Geng

;

Jicheng Geng b)

(Writing – original draft)

Harbin Engineering University

, Harbin,

China

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Shaolong Han

Shaolong Han c)

(Writing – original draft)

Harbin Engineering University

, Harbin,

China

c)Author to whom correspondence should be addressed: algebra@hrbeu.edu.cn

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Author & Article Information

c)Author to whom correspondence should be addressed: algebra@hrbeu.edu.cn

a)

Electronic mail: fanzhaobing@hrbeu.edu.cn

b)

Electronic mail: jcgeng@hrbeu.edu.cn

J. Math. Phys. 64, 101703 (2023)

Article history

Received:

July 02 2023

Accepted:

September 28 2023

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Citation

Zhaobing Fan, Jicheng Geng, Shaolong Han; Differential operator realization of braid group action on ıquantum groups. J. Math. Phys. 1 October 2023; 64 (10): 101703. https://doi.org/10.1063/5.0166060

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We construct a unique braid group action on deformed q-Weyl algebra Aq(S). Under this action, we give a realization of the braid group action on quasi-split ıquantum groups U(S)ı of type AIII. Furthermore, we directly construct a unique braid group action on polynomial ring P which is compatible with the braid group action on Aq(S) and U(S)ı.

Topics

Associative algebra, Algebraic structures, Representation theory

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2023

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