9 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…
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…
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…
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…
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 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…