13 citations · 35 across the 14 of their papers we have counts for
14 papers
Relative braid group symmetries on quantum supersymmetric pairs of type sAIII
Yaolong Shen, Weinan Zhang
We introduce the relative Coxeter groupoid and construct intrinsic relative braid group symmetries for quantum supersymmetric pairs of type sAIII. These symmetries are constructed…
Representations of quantum symmetric pairs at roots of unity
Jinfeng Song, Weinan Zhang
Let be an involution of a complex semisimple Lie algebra and be the associated quantum symmetric pair at an odd root of unit…
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 …
Quantum Howe duality and Schur duality of type AIII
Weinan Zhang
We establish a new connection between the iHowe duality of type AIII established by Luo-Xu and the iSchur duality established by Bao-Wang. We show that iweight space i…
Relative braid group symmetries on modified iquantum groups and their modules
Weiqiang Wang, Weinan Zhang
We present a comprehensive generalization of Lusztig's braid group symmetries for quasi-split iquantum groups. Specifically, we give 3 explicit rank one formulas for symmetries act…
A Drinfeld type presentation of twisted Yangians of quasi-split type
Kang Lu, Weinan Zhang
We formulate a family of algebras, twisted Yangians (of simply-laced quasi-split type) in Drinfeld type current generators and defining relations. These new algebras admit PBW 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…
Affine quantum groups and twisted Yangians in Drinfeld presentations
Kang Lu, Weiqiang Wang, Weinan Zhang
We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine quantum g…
Braid group action and quasi-split affine quantum groups II: higher rank
Ming Lu, Weiqiang Wang, Weinan Zhang
This paper studies quantum symmetric pairs associated with quasi-split Satake diagrams of affine type $A_{2r-1}, D_r, E_{6}…
A Drinfeld type presentation of twisted Yangians
Kang Lu, Weiqiang Wang, Weinan Zhang
We develop a Gauss decomposition approach to establish a Drinfeld type current presentation for Olshanski's twisted Yangians associated to the orthogonal Lie algebras (also called…
Relative braid group symmetries on quantum groups of Kac-Moody type
Weinan Zhang
Recently, relative braid group actions on quantum groups of arbitrary finite types have been constructed by Wang and the author. In this paper, we extend that construction…
Braid group action and quasi-split affine quantum groups I
Ming Lu, Weiqiang Wang, Weinan Zhang
This is the first of two papers on quasi-split affine quantum symmetric pairs , focusing on t…
An intrinsic approach to relative braid group symmetries on quantum groups
Weiqiang Wang, Weinan Zhang
We initiate a general approach to the relative braid group symmetries on (universal) quantum groups, arising from quantum symmetric pairs of arbitrary finite types, and the…
A Drinfeld type presentation of affine quantum groups II: split BCFG type
Weinan Zhang
Recently, Lu and Wang formulated a Drinfeld type presentation for quantum group arising from quantum symmetric pairs of split affine ADE type…