Generalized universal characters, generalized B-type universal characters, and generalized symplectic universal characters

We discuss the construction of the vertex operator realizations of generalized universal characters, generalized B-type universal characters, and generalized symplectic universal characters. By applying a series of vertex operators to the constant function \(1\), the generating functions of the three symmetric functions are obtained. Furthermore, we investigate three hierarchies respectively satisfied by the three generalized universal characters. In view of the algebraic structure of the three symmetric functions, the generalized universal characters and generalized symplectic universal characters can be expressed in the form related to fermion vacuum expectation values. In addition, a novel boson–fermion correspondence is established.