Ghost Symmetries and Multi-fold Darboux Transformations of Extended Toda Hierarchy

Abstract

In this paper, the author constructs ghost symmetries of the extended Toda hierarchy with their spectral representations. After this, two kinds of Darboux transformations in different directions and their mixed Darboux transformations of this hierarchy are constructed. These symmetries and Darboux transformations might be useful in Gromov-Witten theory of ℂP ¹.

Keywords

Extended Toda hierarchy / Ghost symmetry / Spectral representations / Hirota quadratic equation / Darboux transformation