The symmetric KP hierarchy and affine Yangian of [formula omitted

Abstract

The symmetric functions Yλ(x) are a generalization of Schur functions Sλ(x), and Yλ(x) are symmetric about the x-axis and y-axis. As the Schur functions can be used to describe the tau functions of the KP hierarchy, in this paper, we define the symmetric KP hierarchy whose tau functions can be represented by Yλ(x). The method we use is affine Yangian of gl(1). We also define the Boson-Fermion correspondence in the symmetric KP hierarchy.