Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras

Berenstein and Zelevinsky introduced quantum cluster algebras [3] and the triangular bases [4]. The support conjecture in [12] asserts that the support of a triangular basis element for a rank-2 cluster algebra is bounded by an explicitly described region that is possibly concave. In this paper, we prove the support conjecture for all skew-symmetric rank-2 cluster algebras.& COPY; 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, the support conjecture for all skew-symmetric rank-2 cluster algebras is proven.