Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters |
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| Institution: | School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China |
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| Abstract: | 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. |
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| Keywords: | quantum fields generating functions integrable systems symmetric functions boson-fermion correspondence |
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