Quantum Cluster Characters

Details Quantum Cluster Characters Quantum Cluster Characters

2011-09-29

arxiv.org/abs/1109.6694v1

Mathematics

Quantum Algebra

Scientific paper

Let $\FF$ be a finite field and $(Q,\bfd)$ an acyclic valued quiver. We prove the main conjecture of \cite{rupel}: that the quantum cluster character gives a bijection from the indecomposable rigid valued representations of $Q$ to the set of non-initial quantum cluster variables for the quantum cluster algebra $\cA_{|\FF|}(Q,\Lambda)$. As a corollary we find that for any rigid valued representation $M$ of $Q$ all Grassmannians of subrepresentations $Gr_\bfe^M$ have counting polynomials, allowing for the specialization argument of Hubery.

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