Quantum cluster characters for valued quivers

Dylan Rupel
2015 Transactions of the American Mathematical Society  
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 $\cA_{|\FF|}(\tilde{B},\Lambda)$. As a corollary we find that, for any rigid valued
more » ... d valued representation $V$ of $Q$, all Grassmannians of subrepresentations $Gr_\bfe^V$ have counting polynomials.
doi:10.1090/s0002-9947-2015-06251-5 fatcat:mkba3pxo4nasjckdt5j5ughqae