Quantum fields presentation for orthogonal Schur functions and orthogonal universal characters

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 tau 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.

Automated summary

This paper presents the construction of quantum fields presentation and generating functions for orthogonal Schur functions and orthogonal universal characters (OUC). The boson-fermion correspondence for these two symmetric functions is discussed. Based on the quantum fields presentation, two integrable systems, namely orthogonal KP hierarchy (OKP) and OUC hierarchy, are obtained, with orthogonal Schur functions and orthogonal universal characters as their tau functions respectively. Furthermore, the (m, n)-soliton solution of the OUC hierarchy is discussed. Modified OKP and OUC hierarchies as extensions of integrable systems are also derived.