The Orthogonal and Symplectic Schur Functions, Vertex Operators and Integrable Hierarchies

In this paper, we first construct an integrable system whose solutions include the orthogonal Schur functions and the symplectic Schur functions. We find that the orthogonal Schur functions and the symplectic Schur functions can be obtained by one kind of Boson-Fermion correspondence which is slightly different from the classical one. Then, we construct a universal character which satisfies the bilinear equation of a new infinite-dimensional integrable orthogonal UC hierarchy. (C) 2021 The Authors. Published by Atlantis Press B.V.

Automated summary

In this paper, an integrable system is constructed with solutions including orthogonal Schur functions and symplectic Schur functions. It is found that these functions can be obtained through a Boson-Fermion correspondence which differs slightly from the classical one. Additionally, a universal character satisfying the bilinear equation of a new infinite-dimensional integrable orthogonal UC hierarchy is constructed.