4 papers
Dual and double canonical bases of quantum groups
Ming Lu, Xiaolong Pan
Qin established the geometric realization of entire quantum groups via perverse sheaves, which further give rise to dual canonical bases with integral and positive structure consta…
Dual canonical bases of quantum groups and quantum groups II: geometry
Ming Lu, Xiaolong Pan
The quantum groups admit two realizations: one via the Hall algebras and the other via the quantum Grothendieck rings of quiver varieties, as developed by the first…
Braid group action and quasi-split affine iquantum groups III
Ming Lu, Xiaolong Pan, Weiqiang Wang +1
This is the last of three papers on Drinfeld presentations of quasi-split affine iquantum groups , settling the remaining type …
PBW bases for quantum groups
Ming Lu, Ruiqi Yang, Weinan Zhang
We establish PBW type bases for quantum groups of arbitrary finite type, using the relative braid group symmetries. Explicit formulas for root vectors are provided for $\im…