209 citations · 1.5k across the 128 of their papers we have counts for
70 papers · 1 filter
The nil-Brauer category
Jonathan Brundan, Weiqiang Wang, Ben Webster
We introduce the nil-Brauer category and prove a basis theorem for its morphism spaces. This basis theorem is an essential ingredient required to prove that nil-Brauer categorifies…
Quantum symmetric pairs
Weiqiang Wang
This is a survey of some recent progress on quantum symmetric pairs and applications. The topics include quasi K-matrices, Schur duality, canonical bases, super Kazhdan-Lus…
PBW bases for modified quantum groups
Weiqiang Wang
We construct a basis for a modified quantum group of finite type, extending the PBW bases of positive and negative halves of a quantum group. Generalizing Lusztig's classic results…
Schur duality and Kazhdan-Lusztig basis expanded
Yaolong Shen, Weiqiang Wang
Expanding the classic works of Kazhdan-Lusztig and Deodhar, we establish bar involutions and canonical (i.e., quasi-parabolic KL) bases on quasi-permutation modules over the type B…
Hall algebra of Jordan quiver and Hall-Littlewood functions
Ming Lu, Shiquan Ruan, Weiqiang Wang
We show that the Hall algebra of the Jordan quiver is a polynomial ring in infinitely many generators and obtain transition relations among several generating sets. We esta…
Lectures on dualities ABC in representation theory
Li Luo, Weiqiang Wang
In these lecture notes for a summer mini-course, we provide an exposition on quantum groups and Hecke algebras, including (quasi) R-matrix, canonical basis, and -Schur duality.…
Hall algebra of the projective line and -Onsager algebra
Ming Lu, Shiquan Ruan, Weiqiang Wang
The Hall algebra of the projective line is by definition the twisted semi-derived Ringel-Hall algebra of the category of -periodic complexes of coherent sheaves on the p…
A Drinfeld type presentation of affine quantum groups I: split ADE type
Ming Lu, Weiqiang Wang
We establish a Drinfeld type new presentation for the quantum groups arising from quantum symmetric pairs of split affine ADE type, which includes the -Onsager algebra a…
Hall algebras and quantum symmetric pairs of Kac-Moody type
Ming Lu, Weiqiang Wang
We extend our Hall algebra construction from acyclic to arbitrary quivers, where the quiver algebras are infinite-dimensional 1-Gorenstein in general. Then…
Cells in affine q-Schur algebras
Weideng Cui, Li Luo, Weiqiang Wang
We develop algebraic and geometrical approaches toward canonical bases for affine q-Schur algebras of arbitrary type introduced in this paper. A duality between an affine q-Schur a…
Serre-Lusztig relations for quantum groups
Xinhong Chen, Ming Lu, Weiqiang Wang
Let be a quantum symmetric pair of Kac-Moody type. The quantum groups and the universal quantum groups $\widetilde{\bf U}^\im…
Hall algebras and quantum symmetric pairs III: Quiver varieties
Ming Lu, Weiqiang Wang
The quiver algebras were introduced recently by the authors to provide a Hall algebra realization of universal quantum groups, which is a generalization of Bridgela…
Hall algebras and quantum symmetric pairs II: reflection functors
Ming Lu, Weiqiang Wang
Recently the authors initiated an Hall algebra approach to (universal) quantum groups arising from quantum symmetric pairs. In this paper we construct and study BGP…
Odd singular vector formula for general linear Lie superalgebras
Jie Liu, Li Luo, Weiqiang Wang
We establish a closed formula for a singular vector of weight in the Verma module of highest weight for Lie superalgebra when is atypical with re…
Hall algebras and quantum symmetric pairs I: foundations
Ming Lu, Weiqiang Wang
A quantum symmetric pair consists of a quantum group and its coideal subalgebra with parameters (called an …
A Serre presentation for the quantum groups
Xinhong Chen, Ming Lu, Weiqiang Wang
Let be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where "quasi-split" means the corresponding Satake diagram contains no black node.…
Formulae of -divided powers in , II
Weiqiang Wang, Collin Berman
The coideal subalgebra of the quantum is a polynomial algebra in a generator which depends on a parameter . The existence of the -canonical basis (…
Stability of the centers of group algebras of
Jinkui Wan, Weiqiang Wang
The center of the integral group algebra of the general linear group over a finite field admits a filtration with respect to the reflection length. We…
Character formulae in category for exceptional Lie superalgebra
Shun-Jen Cheng, Weiqiang Wang
We classify the blocks, compute the Verma flags of tilting and projective modules in the BGG category for the exceptional Lie superalgebra . The projective injec…
Quantum Schur duality of affine type C with three parameters
Zhaobing Fan, Chun-Ju Lai, Yiqiang Li +3
We establish a three-parameter Schur duality between the affine Hecke algebra of type C and a coideal subalgebra of quantum affine . At the equal parameter special…
Modular representations of exceptional supergroups
Shun-Jen Cheng, Bin Shu, Weiqiang Wang
We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.
The -Schur algebras and -Schur dualities of finite type
Li Luo, Weiqiang Wang
We formulate a -Schur algebra associated to an arbitrary -invariant finite set of integral weights for a complex simple Lie algebra with Weyl group . We es…
Spin nilHecke algebras of classical type
Ian Johnson, Weiqiang Wang
We formulate and study the spin nilHecke algebras and of type B/D, which differ from the usual nilHecke al…
Character formulae in category for exceptional Lie superalgebras
Shun-Jen Cheng, Weiqiang Wang
We establish character formulae for representations of the one-parameter family of simple Lie superalgebras . We provide a complete description of the Verma flag multipli…