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Explicit cluster multiplication formulas for the quantum cluster algebra of type $A_2^{(1)}$ (2504.10182v1)
Published 14 Apr 2025 in math.QA and math.RT
Abstract: Let $Q$ be an affine quiver of type $A_2{(1)}$. We explicitly construct the cluster multiplication formulas for the quantum cluster algebra of $Q$ with principal coefficients. As applications, we obtain: (1)\ an exact expression for every quantum cluster variable as a polynomial in terms of the quantum cluster variables in clusters which are one-step mutations from the initial cluster; (2)\ an explicit bar-invariant positive $\mathbb{ZP}$-basis.
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