Dimers, crystals and quantum Kostka numbers

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

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• ISSN: 1286-4889
• 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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