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Bibliographic Details
Main Authors: Le, Ian, Yıldırım, Emine
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.14501
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Table of Contents:
  • The homogeneous coordinate ring of the Grassmannian $\rm{Gr}(k,n)$ has a well-known cluster structure. There is a categorification of this cluster structure via a category of modules for a ring $A_{k,n}$ due to Jensen-King-Su, building on work of Geiss-Leclerc-Schröer, in which cluster variables correspond to indecomposable rigid modules. We give a combinatorial description of modules that correspond to rank $2$ cluster variables by using webs. This conjecturally gives the categorification of all rank $2$ cluster variables.