Integrable structure of modified melting crystal model
Mathematical Physics
2012-08-23 v1 High Energy Physics - Theory
math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, "shift symmetries" of a quantum torus algebra plays a central role. With the aid of these algebraic relations, the partition function of the modified model is shown to be a tau function of the 2D Toda hierarchy. We conjecture that this tau function belongs to a class of solutions (the so called Toeplitz reduction) related to the Ablowitz-Ladik hierarchy.
Cite
@article{arxiv.1208.4497,
title = {Integrable structure of modified melting crystal model},
author = {Kanehisa Takasaki},
journal= {arXiv preprint arXiv:1208.4497},
year = {2012}
}
Comments
10 pages, no figure, poster presentation at conference "Integrability in Gauge and String Theory" (August 20-24, 2012)