30 citations · 75 across the 21 of their papers we have counts for
12 papers · 1 filter
Differential operator realization of braid group action on quantum groups
Zhaobing Fan, Jicheng Geng, Shaolong Han
We construct a unique braid group action on modified -Weyl algebra . Under this action, we give a realization of the braid group action on quasi-split qu…
Young wall construction of level-1 highest weight crystals over and
Zhaobing Fan, Shaolong Han, Seok-Jin Kang +1
With the help of path realization and affine energy function, we give a Young wall construction of level-1 highest weight crystals over and $U_{q}(D_{4}…
Crystal bases and canonical bases for quantum Borcherds-Bozec algebras
Zhaobing Fan, Shaolong Han, Seok-Jin Kang +1
Let be the negative half of a quantum Borcherds-Bozec algebra and be the irreducible highest weight module with . I…
Abstract crystals for quantum Borcherds-Bozec algebras
Zhaobing Fan, Seok-Jin Kang, Young Rock Kim +1
In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crys…
Classical limit of quantum Borcherds-Bozec algebras
Zhaobing Fan, Seok-Jin Kang, Young-Rock Kim +1
Let be a Borcherds-Bozec algebra, be its universal enveloping algebra and be the corresponding quantum Borcherds-Bozec algebr…
Equivariant K-theory approach to -quantum groups
Zhaobing Fan, Haitao Ma, Husileng Xiao
Various constructions for quantum groups have been generalized to -quantum groups. Such generalization is called -program. In this paper, we fill one of parts in th…
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…
Affine flag varieties and quantum symmetric pairs
Zhaobing Fan, Chun-Ju Lai, Yiqiang Li +2
The quantum groups of finite and affine type admit geometric realizations in terms of partial flag varieties of finite and affine type . Recently, the quantum group associat…
Geometric Schur Duality of Classical Type, II
Zhaobing Fan, Yiqiang Li
We establish algebraically and geometrically a duality between the Iwahori-Hecke algebra of type D and two new quantum algebras arising from the geometry of N-step isotropic flag v…
A geometric setting for quantum osp(1|2)
Zhaobing Fan, Yiqiang Li
A geometric categorification is given for arbitrary-large-finite-dimensional quotients of quantum osp(1|2) and the tensor product of its simple modules. The modified quantum osp(1|…
Two-parameter quantum algebras, canonical bases and categorifications
Zhaobing Fan, Yiqiang Li
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-…
Geometric approach to Hall algebra of representations of Quivers over local ring
Zhaobing Fan
By using perverse sheaves on representation spaces of quivers over and jet schemes over flag varieties, we construct a geometric composition algebra under…