Nakajima's quiver varieties and triangular bases of bipartite cluster algebras

2024/05/13 by Li, Li
#16G20 #32S60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 13F60 #Representation Theory (math.RT) #Secondary 14F06

paper · doi:10.48550/arxiv.2405.08234

Abstract

Berenstein and Zelevinsky introduced quantum cluster algebras \citeBZ1 and the triangular bases \citeBZ2. The support conjecture proposed in \citeLLRZ, 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 \citeL 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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