The extended D-Toda hierarchy

• Jipeng Cheng ^[1] ; Todor Milanov ^[2]
  1. [1] China University of Mining and Technology

     China University of Mining and Technology

     China

     
  2. [2] University of Tokyo

     University of Tokyo

     Japón

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 2, 2021
• Idioma: inglés
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• Resumen

  • In a companion paper (arXiv:1910.03150) to this one, we proved that the Gromov–Witten theory of a Fano orbifold line of type D is governed by a system of Hirota Bilinear Equations. The goal of this paper is to prove that every solution to the Hirota Bilinear Equations determines a solution to a new integrable hierarchy of Lax equations. We suggest the name extended D-Toda hierarchy for this new system of Lax equations, because it should be viewed as the analogue of Carlet’s extended bi-graded Toda hierarchy, which is known to govern the Gromov–Witten theory of Fano orbifold lines of type A.