Dimers, crystals and quantum Kostka numbers
Combinatorics
2019-07-02 v1 Mathematical Physics
Algebraic Geometry
math.MP
Representation Theory
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.
Cite
@article{arxiv.1702.07162,
title = {Dimers, crystals and quantum Kostka numbers},
author = {Christian Korff},
journal= {arXiv preprint arXiv:1702.07162},
year = {2019}
}
Comments
12 pages,4 figures, extended abstract for FPSAC 2017, London (accepted)