Geometry of Moduli Spaces and its Application to Infinite Analysis

模空间几何及其在无限分析中的应用

• 批准号: 19340007
• 负责人: UENO Kenji
• 金额: $ 11.65万
• 依托单位: Tokyo Metropolitan University (2010)Yokkaichi University (2009)Kyoto University (2007-2008)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340007/
• 关键词: 代数科学; 共形場理論; モジュラー函手; 位相的場の理論; タイヒミュラー; GNS構成法; ゲージ対称性; 分岐被覆; 剛幾何学; モジュライ空; 無限可積分系; 代数多様体の退化; 重複ファイバー; トロピカル幾何学; 変形パラメータ; 導来圏; モジュライ空間; 接続; ゲージ理論; 代数曲線; 退化; ユニタリ性; 写像類群; 射影的平坦接続; Hitchin接続; p進剛幾何学; ペンローズ変換

From conformal field theory with gauge symmetry constructed by Tsuchiya, Yamada and Ueno I and Joergen E. Andersen constructed modular functors so that we had topological filed theory for three manifolds. When the Lie algebra for gauge symmetry is sl(n, C) we proved that our topological field is isomorphic to the one constructed by Reshetikhin and Turaev by using GNS construction of representations of Hecke algebra. As a corollary to our proof we could also prove that conformal block bundles on the Teichmueller space of pointed Riemann surfaces of genus 0 carry unitary structure compatible with KZ connections.Ueno also constructed a family of curves over a field of characteristic p, which contain multiple fiber pD where D is any divisor appearing a degeneration of a family of curves of genus 2 and p is any prime number.

从Tsuchiya，Yamada和Ueno I和Joergen E. Andersen构建的量规对称性的保形场理论中，我们对三个流形的拓扑提交了拓扑函数。当仪表对称性的谎言代数为SL（N，C）时，我们证明了我们的拓扑领域是与Reshetikhin和Turaev构建的拓扑领域同构的，它使用GNS构造Hecke代数的表示。 As a corollary to our proof we could also prove that conformal block bundles on the Teichmueller space of pointed Riemann surfaces of genus 0 carry unitary structure compatible with KZ connections.Ueno also constructed a family of curves over a field of characteristic p, which contain multiple fiber pD where D is any divisor appearing a degeneration of a family of curves of genus 2 and p is any prime number.

项目成果

Loop spaces and conformal field theory

环空间和共形场论

• 发表时间: 2009
• 作者: Andersen;J. E. & Ueno;K.;Hiraku Nakajima;J.E. Andersen & K. Ueno;上野健爾;Yuji Shimizu
• 通讯作者: Yuji Shimizu

Hecke algebra at root of unity and quantum invariants of three-manifolds

统一根的赫克代数和三流形的量子不变量

• 发表时间: 2010
• 作者: Andersen;J. E. & Ueno;K.;Hiraku Nakajima;J.E. Andersen & K. Ueno;上野健爾
• 通讯作者: 上野健爾

Fields Institute Monographs, 24.

菲尔兹研究所专着，24。

• 发表时间: 2008
• 作者: Kato;F.;Fumiharu Kato;Tsuyoshi Kato;K. Ueno;Kenji Ueno;Kenji Ueno
• 通讯作者: Kenji Ueno

Abelian Conformal Field Theory and Determinant Bundles

阿贝尔共形场论和行列式束

• 发表时间: 2007
• 期刊: International J. Math
• 作者: Andersen;J. E. & Ueno;K.
• 通讯作者: K.

Grassmann structure in the XXZ model. II. Cretion operators.

XXZ 模型中的 Grassmann 结构。

• 发表时间: 2009
• 期刊: Comm. Math Phys. 286-3
• 作者: Boos;H.;Jimbo;M.;Miwa;T.;Smirnov;F.;Takeyama;Y. Hidden
• 通讯作者: Y. Hidden