Toda Tau Functions with Quantum Torus Symmetries

K. Takasaki


The quantum torus algebra plays an important role in a special class of solutions of the Toda hierarchy. Typical examples are the solutions related to the melting crystal model of topological strings and 5D SUSY gauge theories. The quantum torus algebra is realized by a 2D complex free fermion system that underlies the Toda hierarchy, and exhibits mysterious “shift symmetries”. This article is based on collaboration with Toshio Nakatsu.


Toda hierarchy; melting crystal model; quantum torus algebra

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague