3 papers
math.QA2023
Invariant theory of quantum groups of type AIII
Li Luo, Zheming Xu
We develop an invariant theory of quasi-split quantum groups of type AIII on a tensor space associated to Howe dualities. The first and second…
math.RT2023
Asymptotic Schur algebras and cellularity of q-Schur algebras
Weideng Cui, Li Luo, Zheming Xu
We prove that the q-Schur algebras of finite type introduced in [LW22] are cellular in the sense of Graham and Lehrer, which is a generalization of Geck's theorem on the cellularit…
math.RT2021
Geometric Howe dualities of finite type
Li Luo, Zheming Xu
We develop a geometric approach toward an interplay between a pair of quantum Schur algebras of arbitrary finite type. Then by Beilinson-Lusztig-MacPherson's stabilization procedur…