Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of CP¹ orbifolds

الأصل · EN

We prove that the Hirota quadratic equations of Milanov and Tseng define an integrable hierarchy which is equivalent to the extended bigraded Toda hierarchy. In particular this proves a conjecture of Milanov-Tseng that relates the total descendent potential of the orbifold Cₖ,ₘ with a tau function of the bigraded Toda hierarchy.