Toda tau functions with quantum torus symmetries

Understand

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.