Rational reductions of the 2D-Toda hierarchy and mirror symmetry

@article{Brini2014RationalRO,
  title={Rational reductions of the 2D-Toda hierarchy and mirror symmetry},
  author={Andrea Brini and Guido Carlet and Stefano Romano and Paolo Rossi},
  journal={Journal of the European Mathematical Society},
  year={2014},
  volume={19},
  pages={835-880}
}
We introduce and study a two-parameter family of symmetry reductions of the two-dimensional Toda lattice hierarchy, which are characterized by a rational factorization of the Lax operator into a product of an upper diagonal and the inverse of a lower diagonal formal difference operator. They subsume and generalize several classical 1 + 1 integrable hierarchies, such as the bigraded Toda hierarchy, the Ablowitz-Ladik hierarchy and E. Frenkel's q-deformed Gelfand-Dickey hierarchy. We establish… 

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