7 papers
Quiver varieties and dual canonical bases
Ming Lu, Xiaolong Pan
We survey some recent developments on the theory of dual canonical bases for quantum groups and quantum groups. The quiver algebras were introduced by Wang and the…
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…
Dual canonical bases of quantum groups and quantum groups I: Hall algebras
Ming Lu, Xiaolong Pan
The quantum groups have two realizations: one via the Hall algebras and the other via the quantum Grothendieck rings of quiver varieties, as developed by the first…
iQuantum groups and iHopf algebras II: dual canonical bases
Jiayi Chen, Ming Lu, Xiaolong Pan +2
Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of a…
iQuantum groups and iHopf algebras I: foundation
Jiayi Chen, Ming Lu, Xiaolong Pan +2
We introduce the notion of iHopf algebra, a new associative algebra structure defined on a Hopf algebra equipped with a Hopf pairing. The iHopf algebra on a Borel quantum group end…