Study of generalized Verma modules

广义Verma模块的研究

• 批准号: 20540011
• 负责人: MATUMOTO Hisayosi
• 金额: $ 2.75万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540011/
• 关键词: 一般化旗多様体; 半単純リー群; ユニタリ表現; 一般化バルマ加群; 有限W代数; 一般化バルマ; 一般化Verma加群

We classified homomorphisms between scalar generalized modules associated with normal parabolic subalgebras of exceptional Lie algebras under the assumption that the infinitesimal characters are regular integral. We also studied Whittaker modules in the completion of generalized modules associated with parabolic subalgebras including Jacobi parabolic subalgebras of simple Lie algebras of the type C. We also obtained results on irreducibility of the Whittaker dual of principal series representations. We supported 49th joint Symposium on Real Analysis and Functional Analysis.

在无穷小特征是正则积分的假设下，我们对与异常李代数的正常抛物线子代数相关的标量广义模之间的同态进行了分类。我们还研究了与抛物型子代数（包括 C 型简单李代数的雅可比抛物型子代数）相关的广义模的补全中的 Whittaker 模。我们还获得了主级数表示的 Whittaker 对偶不可约性的结果。我们支持第49届实分析和泛函分析联合研讨会。

项目成果

Conference in honor of Toshio Oshima's 60th birthday "Differential Equations and Symmetric Spaces

纪念大岛敏夫 60 岁生日的会议“微分方程和对称空间”

• 发表时间: 2009
• 作者: On homomorphisms between scalar generalized Verma modules

On homomorphisms between scalar generalized Verma modules,

关于标量广义 Verma 模之间的同态，

• 发表时间: 2009
• 作者: 五十嵐誠一(共著);松本久義
• 通讯作者: 松本久義

On exisitence of homomorphisms between generfalized Verma modules

论广义Verma模块之间同态的存在性

• 发表时间: 2009
• 作者: Matumoto;Hisayosi
• 通讯作者: Hisayosi

The 9th workshop on Nilpotent Orbits and Representation Theory

第九届幂零轨道与表示论研讨会