Quantum Cluster Characters

Abstract

Let $\FF$ be a finite field and $(Q,\bfd)$ an acyclic valued quiver with associated exchange matrix $\tilde{B}$. We follow Hubery's approach \cite{hub1} to prove our main conjecture of \cite{rupel}: the quantum cluster character gives a bijection from the isoclasses of indecomposable rigid valued representations of $Q$ to the set of non-initial quantum cluster variables for the quantum cluster algebra $\cA_{|\FF|}(\tilde{B},Λ)$. As a corollary we find that, for any rigid valued representation $V$ of $Q$, all Grassmannians of subrepresentations $Gr_\bfe^V$ have counting polynomials.

material reorganized, some proofs rewritten

References in corpus (4)

• Proof of the Kontsevich Non-Commutative Cluster Positivity Conjecture
• On Quantum Analogue of The Caldero-Chapoton Formula
• A quantum analogue of generic bases for affine cluster algebras
• Quantum Cluster Variables via Serre Polynomials

Cited by in corpus (5)

• Rigid modules and Schur roots
• Quivers with relations for symmetrizable Cartan matrices V. Caldero-Chapoton formula
• Quantum cluster algebras from unpunctured triangulated surfaces: arbitrary coefficients and quantization
• On Generalized Minors and Quiver Representations
• Affine cluster monomials are generalized minors