Nakajima's quiver varieties and triangular bases of bipartite cluster algebras
Abstract
Berenstein and Zelevinsky introduced quantum cluster algebras BZ1 and the triangular bases BZ2. The support conjecture proposed in 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 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.