This article is cited in 6 papers

Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras

Shogo Fujiwara, Yasuaki Gyoda

Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602 Japan

Abstract: We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the maximal degree matrices of the $F$-polynomials called the $F$-matrices and show that the $F$-matrices have the self-duality which is analogous to the duality between the $C$- and $G$-matrices.

Keywords: cluster algebra, mutation, duality.

MSC: 13F60

Received: October 16, 2018; in final form May 10, 2019; Published online May 15, 2019

Language: English

DOI: 10.3842/SIGMA.2019.040

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ArXiv: 1808.02156