Locally free Caldero-Chapoton functions for rank 2 cluster algebras

Abstract: Associated to any acyclic skew-symmetrizable matrix B and a symmetrizer, Geiss, Leclerc and Schröer have defined a finite-dimensional algebra H over any field. Many geometric constructions for acyclic quivers carry over to this situation by using complex numbers. They show that in finite types, the non-initial cluster variables (of the cluster algebra associated to B) are exactly the locally free Caldero—Chapoton functions of indecomposable locally free rigid H-modules and conjecture it to be true in general. We verify this conjecture in rank 2 by showing that the locally free F-polynomials of certain modules under reflection functors satisfy the same recursion of the F-polynomials of cluster variables. This is joint work with Daniel Labardini-Fragoso.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

( slides )

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections