5 papers
Construction of PBW and canonical bases in the folding extension algebras for symmetrizable types
Yumeng Wu
We study extension algebras arising from Lusztig's construction of perverse sheaves on quiver representation spaces equipped with an admissible automorphism , leading to folding…
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…
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…