Research
The i-quantum groups, arising from quantum symmetric pairs, are certain coideal subalgebras of quantum groups. The i-quantum groups have applications on (super) Kazhdan-Lusztig theory, Schur duality, geometry, categorification, Hall algebras, and integrable systems. I am currently working on generalizing various results from quantum groups to i-quantum groups. I am specifically interested in the following topics:
Drinfeld type presentations for affine i-quantum groups and twisted Yangians,
representation theory of affine quantum groups and affine i-quantum groups,
relative braid group symmetries on i-quantum groups and on their modules,
quasi K-matrices,
canonical basis and i-canonical basis.
Papers and Preprints
A Drinfeld type presentation of affine i-quantum groups II: split BCFG type, Lett. Math. Phys. 112 (2022) , 89, arXiv:2102.03203.
An intrinsic approach to relative braid group symmetries on i-quantum groups (with Weiqiang Wang), Proc. Lond. Math. Soc. 127 (2023), 1338-1423, published version, arXiv:2201.01803.
Braid group action and quasi-split affine i-quantum groups I (with Ming Lu and Weiqiang Wang), Represent. Theory 27 (2023), 1000-1040, published version, arXiv:2203.11286.
Relative braid group symmetries on i-quantum groups of Kac-Moody type, Selecta Math. 29 (2023), 59, published version, arXiv:2209.12860.
A Drinfeld type presentation of twisted Yangians (with Kang Lu and Weiqiang Wang), submitted, arXiv:2308.12254.
Braid group action and quasi-split affine i-quantum groups II: higher rank (with Ming Lu and Weiqiang Wang), Commun. Math. Phys. 405 (2024), 142, published version, arXiv:2311.10299.
Affine i-quantum groups and twisted Yangians in Drinfeld presentations (with Kang Lu and Weiqiang Wang), submitted, arXiv:2406.05067.
PBW bases for i-quantum groups (with Ming Lu and Ruiqi Yang), submitted, arXiv:2407.13127.
A Drinfeld type presentation of twisted Yangians of quasi-split type (with Kang Lu), submitted, arXiv:2408:06981.