17 citations · 154 across the 69 of their papers we have counts for
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The iterated geometric Green's formula
Chao Shen, Jie Xiao
Fang, Lan, and Xiao established the geometric Green's formula as a categorical isomorphism for arbitrary semisimple complexes. In this short note, we generalize their work to multi…
Sheaf realization of Bridgeland's Hall algebra of Dynkin type
Jiepeng Fang, Yixin Lan, Jie Xiao
As one of results in [6], Bridgeland realized the quantum group via the localization of Ringel-Hall algebra for the two-periodic projective complexes of quiver repre…
The correspondence between the canonical and semicanonical bases
Jiepeng Fang, Yixin Lan, Jie Xiao
Given any symmetric Cartan datum, Lusztig has provided a pair of key lemmas to construct the perverse sheaves over the corresponding quiver and the functions of irreducible compone…
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…
The Parity of Lusztig's Restriction Functor and Green's Formula
Jiepeng Fang, Yixin Lan, Jie Xiao
Our investigation in the present paper is based on three important results. (1) In [12], Ringel introduced Hall algebra for representations of a quiver over finite fields and prove…
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…