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.
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