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Mathematics > Representation Theory
Title: Nakajima's quiver varieties and triangular bases of bipartite cluster algebras
(Submitted on 13 May 2024)
Abstract: Berenstein and Zelevinsky introduced quantum cluster algebras \cite{BZ1} and the triangular bases \cite{BZ2}. The support conjecture proposed in \cite{LLRZ}, which asserts that the support of each triangular basis element for a rank-2 cluster algebra is bounded by an explicitly described region, was established in \cite{L} for skew-symmetric rank-2 cluster algebras. In this paper we extend this result by proving a bound on the support of each triangular basis element for bipartite cluster algebras.
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