13 papers
Associated graded modules of mixed Hodge modules on quivers and preprojective K-theoretic Hall algebra
Yixin Lan
We study the connection between mixed Hodge modules on quiver moduli spaces and the K-theoretic Hall algebra of preprojective algebras by taking associated graded modules. Furtherm…
Structure coefficients for quantum groups
Yixin Lan, Yumeng Wu, Jie Xiao
According to the Hall algebras of quivers with automorphisms under Lusztig's construction, the polynominal forms of several structure coefficients for quantum groups of all finite…
Lusztig sheaves, decomposition rule and restriction rule
Yixin Lan
In this article, we realize the subquotient based modules of certain tensor products or restricted modules via Lusztig's perverse sheaves on multi-framed quivers, and provide a con…
Canonical bases of tensor products of integrable highest weight modules arising from framed constructions
Jiepeng Fang, Yixin Lan
Given a quantum group, we prove that the canonical bases of the tensor products of its integrable highest weight modules can be obtained from the canonical bases of the integrable…
Lusztig sheaves, characteristic cycles and the Borel-Moore homology of Nakajima's quiver varieties
Jiepeng Fang, Yixin Lan
By using characteristic cycles, we build a morphism from the canonical bases of integrable highest weight modules of quantum groups to the top Borel-Moore homology groups of Nakaji…
Lusztig sheaves and integrable highest weight modules in the symmetrizable case
Yixin Lan, Yumeng Wu, Jie Xiao
This paper continues the work of \cite{fang2023lusztigsheavesintegrablehighest} and \cite{fang2023lusztigsheavestensorproducts}. For a symmetrizable generalized Cartan matrix a…
The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism
Jiepeng Fang, Yixin Lan, Yumeng Wu
In [8], Fang-Lan-Xiao proved a formula about Lusztig's induction and restriction functors which can induce Green's formula for the path algebra of a quiver over a finite field via…
Lusztig sheaves and tensor products of integrable highest weight modules
Jiepeng Fang, Yixin Lan
By introducing -framed quivers, we define the localization of Lusztig's sheaves for -framed quivers and functors for localizations. This…
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…