Indecomposable Modules in the Grassmannian Cluster Category ${\rm CM}(B_{5,10})$

Abstract

In this paper we study indecomposable rank 2 modules in the Grassmannian cluster category CM(B5,10). This is the smallest wild case containing modules whose profile layers are 5-interlacing. We construct all rank 2 indecomposable modules with filtration {i, i + 2, i + 4, i + 6, i + 8} | {i + 1, i + 3, i + 5, i + 7, i + 9}, classify them up to isomorphism, and parameterize all infinite families of non-isomorphic rank 2 modules.