Dimers, crystals and quantum Kostka numbers

Korff, C. (2017) Dimers, crystals and quantum Kostka numbers. Seminaire Lotharingien de Combinatoire, 78B.40, 12pp.

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We relate the counting of honeycomb dimer configurations on the cylinder to the counting of certain vertices in Kirillov-Reshetikhin crystal graphs. We show that these dimer configurations yield the quantum Kostka numbers of the small quantum cohomology ring of the Grassmannian, i.e. the expansion coefficients when multiplying a Schubert class repeatedly with different Chern classes. This allows one to derive sum rules for Gromov-Witten invariants in terms of dimer configurations.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Korff, Professor Christian
Authors: Korff, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Seminaire Lotharingien de Combinatoire
Publisher:Universite Louis Pasteur
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Séminaire Lotharingien de Combinatoire, Issue 78B, Proceedings of the 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2017), London, UK, 9-13 July 2017
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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