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π-TYPE FERMIONS AND π-TYPE KP HIERARCHY

Published online by Cambridge University Press:  14 September 2018

NA WANG*
Affiliation:
Department of Mathematics and Statistics, Henan University, Kaifeng 475001, China e-mail: wangna@henu.edu.cn
CHUANZHONG LI*
Affiliation:
Department of Mathematics, Ningbo University, Ningbo 315211, China e-mail: lichuanzhong@nbu.edu.cn

Abstract

In this paper, we first construct π-type Fermions. According to these, we define π-type Boson–Fermion correspondence which is a generalization of the classical Boson–Fermion correspondence. We can obtain π-type symmetric functions Sλπ from the π-type Boson–Fermion correspondence, analogously to the way we get the Schur functions Sλ 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 π-type KP hierarchy and obtain its tau functions.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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