The symmetric KP hierarchy and affine Yangian of gl(1)

The symmetric functions Y-lambda(x) are a generalization of Schur functions S-lambda(x), and Y-lambda (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 Y-lambda(x). The method we use is affine Yangian of gl(1). We also define the Boson-Fermion correspondence in the symmetric KP hierarchy.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP(3).