$\pi$-type Fermions and $\pi$-type KP hierarchy

Abstract

In this paper, we firstly construct $\pi$-type Fermions. According to these, we define $\pi$-type Boson-Fermion correspondence which is a generalization of the classical Boson-Fermion correspondence. We can obtain $\pi$-type symmetric functions $S_\lambda^\pi$ from the $\pi$-type Boson-Fermion correspondence, analogously to the way we get the Schur functions $S_\lambda$ from the classical Boson-Fermion correspondence (which is the same thing as the Jacobi-Trudi formula). Then as a generalization of KP hierarchy, we construct the $\pi$-type KP hierarchy and obtain its tau functions.