Some Consequences of Categorification

Abstract

Several conjectures on acyclic skew-symmetrizable cluster algebras are proven as direct consequences of their categorification via valued quivers. These include conjectures of Fomin-Zelevinsky, Reading-Speyer, and Reading-Stella related to $\mathbf{d}$-vectors, $\mathbf{g}$-vectors, and $F$-polynomials.

References in corpus (3)

• Mutations of group species with potentials and their representations. Applications to cluster algebras
• Polytopal realizations of finite type $\mathbf{g}$-vector fans
• An affine almost positive roots model

Cited by in corpus (1)

• An affine almost positive roots model