5 papers
Lusztig sheaves and integrable highest weight modules
Jiepeng Fang, Yixin Lan, Jie Xiao
We consider the localization of Lusztig's sheaves for framed quivers, and define functors $E^{(n)}_{i},F^{(n)}_{i},K^…
Lie algebras arising from two-periodic projective complex and derived categories
Jiepeng Fang, Yixin Lan, Jie Xiao
Let be a finite-dimensional -algebra of finite global dimension and be the category of finitely generated right -modules. By using of the category…
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…
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…