Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters

doi:10.1088/1674-1056/ac4f57

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.

Keywords: quantum fields generating functions integrable systems symmetric functions boson-fermion correspondence

Received: 23 December 2021
Revised: 23 January 2022
Accepted manuscript online: 27 January 2022

PACS:	02.10.Hh	(Rings and algebras)
	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11965014 and 12061051) and the National Science Foundation of Qinghai Province, China (Grant No. 2021-ZJ-708). The authors gratefully acknowledge the support of Professor Ke Wu and Professor Weizhong Zhao at Capital Normal University, China.

Corresponding Authors: Zhaowen Yan
E-mail: yanzw@imu.edu.cn

Cite this article:

Denghui Li(李登慧), Fei Wang(王菲), and Zhaowen Yan(颜昭雯) Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters 2022 Chin. Phys. B 31 080202

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