209 citations · 1.5k across the 128 of their papers we have counts for
39 papers · 1 filter
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…
Nil-Brauer categorifies the split iquantum group of rank one
Jonathan Brundan, Weiqiang Wang, Ben Webster
We prove that the Grothendieck ring of the monoidal category of finitely generated graded projective modules for the nil-Brauer category is isomorphic to an integral form of the sp…
Hall algebras and quantum groups
Ming Lu, Weiqiang Wang
We survey some recent development on the theory of Hall algebras. Starting from quivers (aka quivers with involutions), we construct a class of 1-Gorenstein algebra…
Formulae of -divided powers in , III
Xinhong Chen, Weiqiang Wang
The -divided powers (depending on a parity) form the canonical basis for the split rank 1 quantum group and they are a basic ingredient for quantum…
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…
Braid group symmetries on quasi-split quantum groups via Hall algebras
Ming Lu, Weiqiang Wang
We establish automorphisms with closed formulas on quasi-split quantum groups of symmetric Kac-Moody type associated to restricted Weyl groups. The proofs are carried out i…
Serre-Lusztig relations for quantum groups III
Xinhong Chen, Ming Lu, Weiqiang Wang
let be a quasi-split universal quantum group associated to a quantum symmetric pair of Kac-Moody…
Serre-Lusztig relations for quantum groups II
Xinhong Chen, Gail Letzter, Ming Lu +1
The Serre relations and the corresponding Serre-Lusztig relations are formulated and established for arbitrary quantum groups arising from quantum symmetric pairs o…
Quantum supergroups VI. Roots of
Christopher Chung, Thomas Sale, Weiqiang Wang
A quantum covering group is an algebra with parameters and subject to and it admits an integral form; it specializes to the usual quantum group at and to a qu…
Canonical bases arising from quantum symmetric pairs of Kac-Moody type
Huanchen Bao, Weiqiang Wang
For quantum symmetric pairs of Kac-Moody type, we construct canonical bases for the highest weight integrable -modules and the…
Canonical bases for tensor products and super Kazhdan-Lusztig theory
Huanchen Bao, Weiqiang Wang, Hideya Watanabe
We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based -module and a based -module is a based $\te…
Canonical bases arising from quantum symmetric pairs
Huanchen Bao, Weiqiang Wang
We develop a general theory of canonical bases for quantum symmetric pairs with parameters of arbitrary finite type. We construct new canonical ba…
Affine Hecke algebras and quantum symmetric pairs
Zhaobing Fan, Chun-Ju Lai, Yiqiang Li +2
We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and af…
Multiparameter quantum Schur duality of type B
Huanchen Bao, Weiqiang Wang, Hideya Watanabe
We establish a Schur type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with 2 parameters. We identify the -canonical…
Modular affine vertex algebras and baby Wakimoto modules
Tomoyuki Arakawa, Weiqiang Wang
We develop some basic properties such as -centers of affine vertex algebras and free field vertex algebras in prime characteristic. We show that the Wakimoto-Feigin-Frenkel homo…
Quantum Shuffles and Quantum Supergroups of Basic Type
Sean Clark, David Hill, Weiqiang Wang
We initiate the study of several distinguished bases for the positive half of a quantum supergroup associated to a general super Cartan datum of…
Quantum Supergroups III. Twistors
Sean Clark, Zhaobing Fan, Yiqiang Li +1
We establish direct connections at several levels between quantum groups and supergroups associated to bar-consistent super Cartan datum by constructing an automorphism (called twi…
Quantum supergroups II. Canonical basis
Sean Clark, David Hill, Weiqiang Wang
Following Kashiwara's algebraic approach, we construct crystal bases and canonical bases for quantum supergroups with no isotropic odd roots and for their integrable modules.
Quantum Supergroups I. Foundations
Sean Clark, David Hill, Weiqiang Wang
In this part one of a series of papers, we introduce a new version of quantum covering and super groups with no isotropic odd simple root, which is suitable for the studies of inte…
Categorification of quantum Kac-Moody superalgebras
David Hill, Weiqiang Wang
We introduce a non-degenerate bilinear form and use it to provide a new characterization of quantum Kac-Moody superalgebras with no isotropic odd simple roots. We show that the spi…
Two-parameter quantum vertex representations via finite groups and the McKay correspondence
Naihuan Jing, Honglian Zhang
We introduce two-parameter quantum toroidal algebras of simply laced types and provide their group theoretic realization using finite subgroups of via McKay corre…
A Fock space approach to representation theory of osp(2|2n)
Shun-Jen Cheng, Weiqiang Wang, R. B. Zhang
A Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are c…
Hilbert schemes of points on the minimal resolution and soliton equations
Zhenbo Qin, Weiqiang Wang
The equivariant and ordinary cohomology rings of Hilbert schemes of points on the minimal resolution C^2//G for cyclic G are studied using vertex operator technique, and connection…
The Bloch-Okounkov correlation functions at higher levels
Shun-Jen Cheng, Weiqiang Wang
We establish an explicit formula for the n-point correlation functions in the sense of Bloch-Okounkov for the irreducible representations of and of…