The fermion representation of the generalized phase model

Abstract

In this paper, we study the (N,N)-particle vector, the general states and the scalar products in the generalized phase model from the fermions point to view. Based on the boson-fermion correspondence, the core relations among the states of the Maya diagram, the Schur functions and the universal characters have been investigated. Moreover, it is proved the scalar products of the (N,N)-particle vectors and the general states in the generalized phase model are the tau functions of the UC hierarchy.