The iquantum groups, arising from quantum symmetric pairs, are certain coideal subalgebras of quantum groups. The iquantum 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 iquantum groups. I am specifically interested in the following topics:
Drinfeld type presentations for affine iquantum groups and twisted Yangians
Relative braid group symmetries on iquantum groups and on their modules
Quasi K-matrices
Canonical basis and i-canonical basis
Poisson algebras arising from quantum groups and quantum symmetric pairs
Quantum groups and quantum symmetric pairs at roots of unity
Papers and Preprints
A Drinfeld type presentation of affine iquantum groups II: split BCFG type, Lett. Math. Phys. 112 (2022) , article no. 89, published version, arXiv:2102.03203.
An intrinsic approach to relative braid group symmetries on iquantum groups (with Weiqiang Wang), Proc. Lond. Math. Soc. 127 (2023), 1338-1423, published version, arXiv:2201.01803.
Braid group action and quasi-split affine iquantum groups I (with Ming Lu and Weiqiang Wang), Represent. Theory 27 (2023), 1000-1040, published version, arXiv:2203.11286.
Relative braid group symmetries on iquantum 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), Represent. Theory, to appear, arXiv:2308.12254.
Braid group action and quasi-split affine iquantum groups II: higher rank (with Ming Lu and Weiqiang Wang), Commun. Math. Phys. 405 (2024), article no. 142, published version, arXiv:2311.10299.
Affine i-quantum groups and twisted Yangians in Drinfeld presentations (with Kang Lu and Weiqiang Wang), Commun. Math. Phys. 406 (2025), article no. 98, published version, arXiv:2406.05067.
PBW bases for iquantum groups (with Ming Lu and Ruiqi Yang), J. Algebra 684 (2025), 441-478, published version, arXiv:2407.13127.
A Drinfeld type presentation of twisted Yangians of quasi-split type (with Kang Lu), submitted, arXiv:2408:06981.
Braid group symmetries on Poisson algebras arising from quantum symmetric pairs (with Jinfeng Song), submitted, arXiv:2507.09456.
Relative braid group symmetries on modified iquantum groups and their modules (with Weiqiang Wang), submitted, arXiv:2508.12041.
Quantum Howe duality and Schur duality of type AIII, submitted.