Quantum fields presentation for orthogonal Schur functions and orthogonal universal characters

Abstract

This paper is concerned with the construction of quantum fields presentation and generating functions of orthogonal Schur functions and orthogonal universal characters (OUC). The boson-fermion correspondence for these two symmetric functions has been presented. Based on the quantum fields presentation, we obtain two integrable systems, namely, orthogonal KP hierarchy (OKP) and OUC hierarchy whose [Formula: see text] functions are orthogonal Schur functions and orthogonal universal characters, respectively. Moveover, the (m, n)-soliton solution of the OUC hierarchy has been discussed. In addition, we derive the modified OKP and OUC hierarchies as extensions of integrable systems.