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

TL;DR

This paper classifies and constructs all indecomposable rank 2 modules in the Grassmannian cluster category ${ m CM}(B_{5,10})$, revealing the structure of modules with 5-interlacing profiles in this minimal wild case.

Contribution

It provides a complete classification and parameterization of all rank 2 indecomposable modules with specific filtration in the smallest wild Grassmannian cluster category.

Findings

Constructed all rank 2 indecomposable modules with given filtration.

Classified modules up to isomorphism.

Parameterization of infinite families of modules.

Abstract

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