87 citations · 223 across the 18 of their papers we have counts for
7 papers · 1 filter
From i-boxes to signed words
Alessandro Contu, Fan Qin, Qiaoling Wei
The combinatorics of i-boxes has recently been introduced by Kashiwara--Kim--Oh--Park in the study of cluster algebras arising from the representation theory of quantum affine alge…
Stability scattering diagrams and quiver coverings
Qiyue Chen, Travis Mandel, Fan Qin
Given a covering of a quiver (with potential), we show that the associated Bridgeland stability scattering diagrams are related by a restriction operation under the assumption of a…
A refined multiplication formula for cluster characters
Bernhard Keller, Pierre-Guy Plamondon, Fan Qin
We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories. This formula generalizes those known for arbitrary pairs…
The valuation pairing on an upper cluster algebra
Peigen Cao, Bernhard Keller, Fan Qin
It is known that many (upper) cluster algebras are not unique factorization domains. We exhibit the local factorization properties with respect to any given seed : any non-zero…
Cluster algebras and their bases
Fan Qin
We give a brief introduction to (upper) cluster algebras and their quantization using examples. Then we present several important families of bases for these algebras using topolog…
Bases for upper cluster algebras and tropical points
Fan Qin
It is known that many (upper) cluster algebras possess different kinds of good bases which contain the cluster monomials and are parametrized by the tropical points of cluster Pois…
Graded quiver varieties, quantum cluster algebras and dual canonical basis
Yoshiyuki Kimura, Fan Qin
Inspired by a previous work of Nakajima, we consider perverse sheaves over acyclic graded quiver varieties and study the Fourier-Sato-Deligne transform from a representation theore…