吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (6): 1285-1290.

• •    下一篇

扭Yangian代数Y(o2)的Verma模

葛万里, 谭易兰, 徐森荣   

  1. 江苏大学 数学科学学院, 江苏 镇江 212013
  • 收稿日期:2024-06-05 出版日期:2024-11-26 发布日期:2024-11-26
  • 通讯作者: 徐森荣 E-mail:senrxu@163.com

Verma Modules of Twisted Yangian Y(o2)

GE Wanli, TAN Yilan, XU Senrong   

  1. School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu Province, China
  • Received:2024-06-05 Online:2024-11-26 Published:2024-11-26

摘要: 考虑扭Yangian代数Y(o2)的Verma模M(μ(u))可约的充分必要条件. 如果M(μ(u))的权由某个有理函数决定, 则通过构造法可得到M(μ(u))的一个真子模, 进而证明M(μ(u))可约; 若M(μ(u))可约, 则可得到一个关于u的有理函数, 从而给出了M(μ(u))可约的必要条件为该有理函数是在u=∞处的Laurent展开.

关键词: 扭Yangian代数, Verma模, 可约性

Abstract: We considered necessary and sufficient conditions for the Verma modules M(μ(u)) of twisted Yangian Y(o2)  to be reducible. If the weight of M(μ(u)) was determined by a certain rational function,  we could obtain a proper submodule of M(μ(u)) through construction method, thus proving  that M(μ(u)) was reducible. If M(μ(u)) was reducible, we could obtain a rational function associated with u,thus  we gave a necessary condition for M(μ(u)) to be reducible was that the rational function was a Laurent expansion at u=∞.

Key words: twisted Yangian, Verma module, reducibility

中图分类号: 

  • O152.5