中国物理B ›› 2025, Vol. 34 ›› Issue (1): 10203-010203.doi: 10.1088/1674-1056/ad925b

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Multiparameter generalized universal characters and multiparameter generalized B-type universal characters

Jingfan Wang(王竸凡), and Zhaowen Yan(颜昭雯)†   

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
  • 收稿日期:2024-10-04 修回日期:2024-11-07 接受日期:2024-11-14 发布日期:2024-12-24
  • 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. 12461048 and 12061051), the Natural Science Foundation of Inner Mongolia Autonomous Region (Grant No. 2023MS01003), and the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No. NJYT23096). Zhaowen Yan acknowledges the financial support from the Program of China Scholarships Council (Grant No. 202306810054) for one year study at the University of Leeds.

Multiparameter generalized universal characters and multiparameter generalized B-type universal characters

Jingfan Wang(王竸凡), and Zhaowen Yan(颜昭雯)†   

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
  • Received:2024-10-04 Revised:2024-11-07 Accepted:2024-11-14 Published:2024-12-24
  • Contact: Zhaowen Yan E-mail:yanzw@imu.edu.cn
  • About author:2025-010203-241442.pdf
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12461048 and 12061051), the Natural Science Foundation of Inner Mongolia Autonomous Region (Grant No. 2023MS01003), and the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No. NJYT23096). Zhaowen Yan acknowledges the financial support from the Program of China Scholarships Council (Grant No. 202306810054) for one year study at the University of Leeds.

摘要: We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character, and by acting the quantum fields presentations to the constant $1$, the generating functions are derived. Furthermore, we introduce two integrable systems known as the generalized UC (GUC) hierarchy and the generalized B-type UC (GBUC) hierarchy satisfied by the generalized universal character and the generalized B-type universal character, respectively. Based on infinite sequences of complex numbers, we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character, which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy, respectively.

关键词: symmetric functions, quantum fields, generating functions, multiparameter generalized universal characters

Abstract: We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character, and by acting the quantum fields presentations to the constant $1$, the generating functions are derived. Furthermore, we introduce two integrable systems known as the generalized UC (GUC) hierarchy and the generalized B-type UC (GBUC) hierarchy satisfied by the generalized universal character and the generalized B-type universal character, respectively. Based on infinite sequences of complex numbers, we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character, which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy, respectively.

Key words: symmetric functions, quantum fields, generating functions, multiparameter generalized universal characters

中图分类号:  (Rings and algebras)

  • 02.10.Hh
02.30.Ik (Integrable systems) 05.45.Yv (Solitons)