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Cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$ (1706.04376v2)
Published 14 Jun 2017 in math.QA, math.RA, and math.RT
Abstract: The objective of the present paper is to prove cluster multiplication theorem in the quantum cluster algebra of type $A_{2}{(2)}$. As corollaries, we obtain bar-invariant $\mathbb{Z}[q{\pm\frac{1}{2}}]$-bases established in [6], and naturally deduce the positivity of the elements in these bases. One bar-invariant basis as the triangular basis of this quantum cluster algebra is also explicitly described.
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