扭Yangian代数Y(o_(2))的Verma模  

Verma Modules of Twisted Yangian Y(o_(2))

作　　者：葛万里 谭易兰 徐森荣 GE Wanli;TAN Yilan;XU Senrong(School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,Jiangsu Province,China)

机构地区：[1]江苏大学数学科学学院,江苏镇江212013

出　　处：《吉林大学学报（理学版）》2024年第6期1285-1290,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12201253);江苏省自然科学基金(批准号:BK20220510);江苏大学高级人才启动基金(批准号:5501190011).

摘　　要：考虑扭Yangian代数Y(o_(2))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.We considered necessary and sufficient conditions for the Verma modules M(μ(u))of twisted Yangian Y(o_(2))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=∞.

关 键 词：扭Yangian代数 VERMA模 可约性 

分 类 号：O152.5[理学—数学]