摘要
This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.
基金
Project supported by the National Natural Science Foundation of China(Grant Nos.11965014 and 12061051)
the National Science Foundation of Qinghai Province,China(Grant No.2021-ZJ-708)。
