Lie theoretic construction of simply elliptic singularities and associated primitive forms

简单椭圆奇点和相关原始形式的李理论构造

• 批准号: 14540054
• 负责人: YAMADA Hiroshi
• 金额: $ 2.24万
• 依托单位: Kitami Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540054/
• 关键词: elliptic curve; double loop Lie algebra; unstable vector bundle; simply elliptic singularity; super Virasoro algebra; Verma module; Fock module; hypergeometric fuction; 楕円型Lie環; 楕円型Weyl群; Atiyah-Bott point; Painleve方程式; 単純楕円型特異点; 単純特異点; パンルベ

There is well known correspondence of isomorphism classes of holomorphic vector bundles over elliptic curves and orbit spaces of double loop algebras with respect to adjoint actions of double loop groups. Using this correspondence and an action of double loop groups on the C^*-bundle on double loop Lie algebras, Yamada have characterized unstable holomorphic vector bundles over elliptic curves. From this results, we will construct simply elliptic singularities in terms of Lie algebras. But this results are obtained under a assumption of existence of double loop group invariant holomorphic functions on C^*-bundle over double loop Lie algebras. So we should prove the existence of them.Watanabe has calculated the degeneration of connection formulas for Gauss hypergeometric functions.Iohara and Koga have studied the structure of Verma modules of N=1 super Virasoro algebras. As applications, they construct Bernstein-Gel'fand-Gel'fand type resolutions. Moreover, they have analyzed the structure of the Fock modules over the N=1 super Virasoro algebras. As an application, they constructed the Bechi-Rouet-Stora-tyutin type resolutions.

双环代数的椭圆曲线和轨道空间上的全纯向量丛的同构类对于双环群的伴随作用存在众所周知的对应关系。利用这种对应关系以及双环李代数上的 C^*-丛上的双环群的作用，Yamada 描述了椭圆曲线上的不稳定全纯向量丛。根据这个结果，我们将用李代数构造简单的椭圆奇点。但这个结果是在双环李代数上的C^*-丛上存在双环群不变全纯函数的假设下获得的。所以我们应该证明它们的存在性。Watanabe计算了高斯超几何函数连接公式的退化。Iohara和Koga研究了N=1超Virasoro代数的Verma模的结构。作为应用，他们构建了 Bernstein-Gel'fand-Gel'fand 类型的分辨率。此外，他们还分析了 N=1 超 Virasoro 代数上的 Fock 模块的结构。作为一个应用程序，他们构建了 Bechi-Rouet-Stora-tyutin 类型的决议。

项目成果

Representation theory of Neveu-Schwarz and Ramond algebras II: Fock modules

Neveu-Schwarz 和 Ramond 代数的表示论 II：Fock 模

• DOI: 10.5802/aif.1992
• 发表时间: 2024-09-13
• 期刊: Annales de l'Institut Fourier
• 作者: K. Iohara;Y. Koga
• 通讯作者: Y. Koga

representation theory of Neveu-Schearz and Ramond algebras II

Neveu-Shearz 和 Ramond 代数的表示论 II

• 发表时间: 2003
• 作者: K.Iohara; Y.Koga
• 通讯作者: Y.Koga

Representation theory of Neveu-Schwarz and Ramond algebras I

Neveu-Schwarz 和 Ramond 代数的表示论 I

• 发表时间: 2003
• 作者: K.Iohara; Y.Koga
• 通讯作者: Y.Koga

Representation theory of Neveu–Schwarz and Ramond algebras I: Verma modules

Neveu·Schwarz 和 Ramond 代数的表示论 I：Verma 模

• DOI: 10.1016/s0001-8708(02)00059-2
• 发表时间: 2003-09-01
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: K. Iohara;Y. Koga
• 通讯作者: Y. Koga