Baur, K, King, A and Marsh, RJ orcid.org/0000-0002-4268-8937 (2016) Dimer models and cluster categories of Grassmannians. Proceedings of the London Mathematical Society, 113 (2). pp. 213-260. ISSN 0024-6115
Abstract
We associate a dimer algebra A to a Postnikov diagram D (in a disk) corresponding to a cluster of minors in the cluster structure of the Grassmannian Gr(k, n). We show that A is isomorphic to the endomorphism algebra of a corresponding Cohen-Macaulay module T over the algebra B used to categorify the cluster structure of Gr(k, n) by Jensen-King-Su. It follows that B can be realised as the boundary algebra of A, that is, the subalgebra eAe for an idempotent e corresponding to the boundary of the disk. The construction and proof uses an interpretation of the diagram D, with its associated plabic graph and dual quiver (with faces), as a dimer model with boundary. We also discuss the general surface case, in particular computing boundary algebras associated to the annulus.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2016, London Mathematical Society. This is an author produced version of a paper published in Proceedings of the London Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. This version may differ from the final published version. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/G007497/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 Jun 2016 10:41 |
Last Modified: | 29 Oct 2016 01:02 |
Published Version: | http://doi.org/10.1112/plms/pdw029 |
Status: | Published |
Publisher: | London Mathematical Society |
Identification Number: | 10.1112/plms/pdw029 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:100835 |