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

doi:10.1088/1674-1056/ac4f57

中国物理B ›› 2022, Vol. 31 ›› Issue (8): 80202-080202.doi: 10.1088/1674-1056/ac4f57

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

Denghui Li(李登慧), Fei Wang(王菲), and Zhaowen Yan(颜昭雯)^†

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

收稿日期:2021-12-23 修回日期:2022-01-23 接受日期:2022-01-27 出版日期:2022-07-18 发布日期:2022-07-18
通讯作者: Zhaowen Yan E-mail:yanzw@imu.edu.cn
基金资助:
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.

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

Denghui Li(李登慧), Fei Wang(王菲), and Zhaowen Yan(颜昭雯)^†

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received:2021-12-23 Revised:2022-01-23 Accepted:2022-01-27 Online:2022-07-18 Published:2022-07-18
Contact: Zhaowen Yan E-mail:yanzw@imu.edu.cn
Supported by:
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.

摘要/Abstract

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.

关键词: quantum fields, generating functions, integrable systems, symmetric functions, boson-fermion correspondence

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.

Key words: quantum fields, generating functions, integrable systems, symmetric functions, boson-fermion correspondence

中图分类号: (Rings and algebras)

02.10.Hh

02.30.Ik (Integrable systems) 05.45.Yv (Solitons)

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[J]. 中国物理B, 2022, 31(8): 80202-080202.

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

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

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