Marsh, RJ orcid.org/0000-0002-4268-8937 and Scott, JS (2016) Twists of Plücker coordinates as dimer partition functions. Communications in Mathematical Physics, 341 (3). pp. 821-884. ISSN 0010-3616
Abstract
The homogeneous coordinate ring of the Grassmannian Grk,n has a cluster structure defined in terms of planar diagrams known as Postnikov diagrams. The cluster corresponding to such a diagram consists entirely of Plucker coordinates. We introduce a twist map on Grk,n, related to the Berenstein-Fomin-Zelevinsky-twist, and give an explicit Laurent expansion for the
twist of an arbitrary Plucker coordinate in terms of the cluster variables associated with a fixed
Postnikov diagram. The expansion arises as a (scaled) dimer partition function of a weighted version of the bipartite graph dual to the Postnikov diagram, modified by a boundary condition determined by the Plucker coordinate. We also relate the twist map to a maximal green sequence.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Springer-Verlag Berlin Heidelberg. This is an author produced version of a paper published in Communications in Mathematical Physics. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-015-2493-7 |
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/C01040X/2 EPSRC EP/G007497/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Oct 2015 14:06 |
Last Modified: | 10 May 2019 15:08 |
Published Version: | http://dx.doi.org/10.1007/s00220-015-2493-7 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00220-015-2493-7 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90576 |