# 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…

## 23 Citations

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In this paper we continue the study of the double ramification hierarchy of [Bur15]. After showing that the DR hierarchy satisfies tau-symmetry we define its partition function as the (logarithm of…

### Tau-Structure for the Double Ramification Hierarchies

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In this paper we continue the study of the double ramification hierarchy of Buryak (Commun Math Phys 336(3):1085–1107, 2015). After showing that the DR hierarchy satisfies tau-symmetry we define its…

### Tau-Structure for the Double Ramification Hierarchies

- MathematicsCommunications in Mathematical Physics
- 2018

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Abstract In the present paper, we formulate a Crepant Resolution Correspondence for open Gromov–Witten invariants (OCRC) of toric Lagrangian branes inside Calabi–Yau 3-orbifolds by encoding the open…

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This paper focuses on different reductions of 2-dimensional (2d-)Toda hierarchy. Symmetric and skew symmetric moment matrices are firstly considered, resulting in the differential relations between…

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### Integrable structures of specialized hypergeometric tau functions By Kanehisa Takasaki

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Okounkov’s generating function of the double Hurwitz numbers of the Riemann sphere is a hypergeometric tau function of the 2D Toda hierarchy in the sense of Orlov and Scherbin. This tau function…

### Integrable structures of specialized hypergeometric tau functions

- Mathematics
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Okounkov's generating function of the double Hurwitz numbers of the Riemann sphere is a hypergeometric tau function of the 2D Toda hierarchy in the sense of Orlov and Scherbin. This tau function…

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Abstract In the present paper, we formulate a Crepant Resolution Correspondence for open Gromov–Witten invariants (OCRC) of toric Lagrangian branes inside Calabi–Yau 3-orbifolds by encoding the open…

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