Symmetric universal character, integrable hierarchy, and affine Yangian of [formula omitted

Abstract

We define a symmetric universal character by using the affine Yangian of gl(1), which is related with a pair of 2D Young diagram which is considered as 3D Young diagrams with only one layer in z-axis direction. We also define the symmetric universal character hierarchy and prove that all symmetric universal characters are tau functions of this integrable hierarchy. Then, we construct the Boson-Fermion correspondence in the symmetric universal character hierarchy and symmetric universal character can be realized through them. Finally, the (m,n)-soliton solution of the symmetric universal character hierarchy is given by vertex operators.