3 citations · 7 across the 12 of their papers we have counts for
12 papers
Reflection Functors For Continuous Quivers Of Type A
Yanxiu Liu, Minghui Zhao
As generalizations of quivers of type A, Igusa-Rock-Todorov in [6] introduced continuous quivers of type A. In this paper, we shall generalize BGP reflection functors to continuous…
Derivation functors and Lusztig's induction functors
Minghui Zhao
Lusztig proved the compatibility of induction functors and restriction functors for Lusztig's perverse sheaves. Fang-Lan-Xiao established a categorification of Green's formula and…
On bases of quantum affine algebras
Jie Xiao, Han Xu, Minghui Zhao
Let be the positive part of the quantum group associated with a generalized Cartan matrix. In the case of finite type, Lusztig constructed the canonical…
Tame quivers and affine bases I: a Hall algebra approach to the canonical bases
Jie Xiao, Han Xu, Minghui Zhao
For quantum group of affine type, Lusztig gave an explicit construction of the affine canonical basis by simple perverse sheaves. In this paper, we construct a bar-invariant basis…
Constructions of highest weight modules of double Ringel-Hall algebras via functions
Minghui Zhao
In [19], Zheng studied the bounded derived categories of constructible -sheaves on some algebraic stacks consisting of the representations of a enlarged quiver…
On purity theorem of Lusztig's perverse sheaves
Jie Xiao, Fan Xu, Minghui Zhao
Let be a finite quiver without loops and be the Lusztig category for any dimension vector . The purpose of this paper is to prove that all Frobenius eigenval…
Geometric realizations of Lusztig's symmetries on the whole quantum groups
Minghui Zhao
In this paper, we shall study the structure of the Grothendieck group of the category consisting of Lusztig's perverse sheaves and give a decomposition theorem of it. By using this…
Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula
Jie Xiao, Fan Xu, Minghui Zhao
In this paper, we generalize the categorifical construction of a quantum group and its canonical basis introduced by Lusztig (\cite{Lusztig,Lusztig2}) to the generic form of the wh…
Geometric realizations of Lusztig's symmetries of symmetrizable quantum groups
Minghui Zhao
The geometric realizations of Lusztig's symmetries of symmetrizable quantum groups are given in this paper. This construction is a generalization of that in [19].
Geometric realizations of Lusztig's symmetries
Jie Xiao, Minghui Zhao
In this paper, we give geometric realizations of Lusztig's symmetries. We also give projective resolutions of a kind of standard modules. By using the geometric realizations and th…
BGP-Reflection Functors and Lusztig's Symmetries of Modified Quantized Enveloping Algebras
Jie Xiao, Minghui Zhao
Let be the quantized enveloping algebra and its modified form. Lusztig gives some symmetries on and . Since the reali…
A parameterization of the canonical bases of affine modified quantized enveloping algebras
Jie Xiao, Minghui Zhao
For symmetrizable Kac-Moody Lie algebra , Lusztig introduced the modified quantized enveloping algebra and its canonical basis in [12]. I…