4 papers
Geometric realization of affine bases: the Kronecker quiver case
Yumeng Wu, Jie Xiao
In this paper, we study the transition matrix between the PBW basis and the canonical basis for the negative part of the quantized enveloping algebra of the Kronecker quiver from a…
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 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…
Tame quivers and affine bases II: nonsimply-laced cases
Jie Xiao, Han Xu
In [Tame_quivers_and_affine_bases_I], we give a Ringel-Hall algebra approach to the canonical bases in the symmetric affine cases. In this paper, we extend the results to general s…