Quantum fields presentation and generating functions of three types of universal characters

In this paper, we construct the quantum fields of three types of universal characters corresponding to partition shapes [Formula: see text], [Formula: see text] and [Formula: see text] and derive the commutation relations of quantum fields. By acting the quantum fields on the constant function [Formula: see text], the generating functions of three types of universal characters have been investigated. Furthermore, we discuss three integrable systems characterized by [Formula: see text]-type, [Formula: see text]-type and [Formula: see text]-type universal characters.