A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an i-quantum group). A quantum group can be viewed as an example of i-quantum groups associated to symmetric pairs of diagonal type. Serre presentations, Serre-Lusztig relations (also called higher order Serre relations), and braid group actions are basic tools to study quantum groups.
In a series of papers, the associate professor Xinhong Chen from Southwest Jiaotong University and her collaborators established Serre presentations and Serre-Lusztig relations for i-quantum groups, by using the i-divided powers introduced by H. Bao and W. Wang. As an application, they obtained the formula of braid goup actions for i-quantum groups.
References.
- Xinhong Chen, Ming Lu and Weqiang Wang, Serre-Lusztig relations for i-quantum groups, Comm. Math. Phys. 382 (2021), 1015-1059.
- Xinhong Chen, Ming Lu and Weiqiang Wang, A Serre presentation for the i-quantum groups, Transform. Groups 26 (2021), 827-857.
- Xinhong Chen, Gail Letzter, Ming Lu, Weiqiang Wang, Serre-Lusztig relations for i-quantum groups II, Lett. Math. Phys. 112 (2022), Paper No. 5.
