Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of \(\mathbb CP^1\) orbifolds (Q2857309)

The authors prove that the Hirota quadratic equations of Milanov and Tseng define an integrable hierarchy which is equivalent to the extended bigraded Toda hierarchy. This work is organized as follows: after a brief introduction, in Section 2, some basic facts about the Hirota quadratic equations for the total descendent potential are recalled. In Section 3, the Hirota equations are rewrited in terms of difference operators. In Section 4, the authors shows that the Hirota equations are actually equivalent to the Sato equations. Some alternative formulations of the Hirota equations are commented in Section 5.