Unified viewpoint for hypergeometric functions and the pentagonal number theorem based on representation theory

基于表示论的超几何函数与五边形数定理的统一观点

• 批准号: 23654050
• 负责人: UMEDA Toru
• 金额: $ 1.33万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23654050/
• 关键词: 超幾何函数; 五角数定理; 表現論; 不変式論; q-analogue; 超幾何級数

The famous pentagonal number theorem by Euler has been extended as the description of the anomaly, that is, the difference of the trace of two matrices of infinite size, which are almost conjugate. Notable examples, among them, are inversion formulas for q-hypergeometric series. We investigate the mechanism behind that phenomena from the invariant-theoretic and representation-theoretic points of view, so that some new horizon for the hypergeometric series is opened. Dual pair theory is the key to withdraw the symmetry, even if it is not apparent.

欧拉著名的五边形数定理被推广为对异常的描述，即两个无限大小矩阵的迹差，它们几乎是共轭的。其中值得注意的例子是q-超几何级数的反演公式。本文从不变量论和表示论的角度探讨了这种现象背后的机理，从而为超几何级数的研究开辟了新的视界。对偶理论是撤销对称性的关键，即使它并不明显。

项目成果

An elliptic extension of Askey-Wilson, polynomials and associated elliptic Schur functions

Askey-Wilson 的椭圆扩展、多项式和相关的椭圆 Schur 函数

• 发表时间: 2013
• 作者: Takafumi Akahori;Slim Ibrahim;Hiroaki Kikuchi;Hayato Nawa;N. Nawata and Y. Watatani;M. Noumi
• 通讯作者: M. Noumi

Cayley-Hamilton 型定理と不変式論

凯莱-汉密尔顿型定理和不变量理论

• 发表时间: 2013
• 作者: T;Kajiwara and Y. Watatani;堤 誉志雄;Senjo Shimizu;T. Ishiwata;Mitsuru Sugimoto;T. Kajiwara and Y. Watatani;伊藤稔
• 通讯作者: 伊藤稔

Remarks on $BC_n$ interpolation functions

关于$BC_n$插值函数的备注

• 发表时间: 2013
• 作者: Takafumi Akahori;Slim Ibrahim;Hiroaki Kikuchi;Hayato Nawa;N. Nawata and Y. Watatani;M. Noumi;Mitsuru Sugimoto;Senjo Shimizu;T. Ishiwata and S. Yazaki;Mitsuru Sugimoto;M. Noumi;T. Kajiwara and Y. Watatani;Senjo Shimizu;M. Noumi
• 通讯作者: M. Noumi

Extensions of the tensor algebra and their applications

张量代数的推广及其应用

• 发表时间: 2008
• 作者: T.K.Ushijima;S.Yazaki;Tetsu Mizumachi;Tetsu Mizumachi;Minoru Itoh;Minoru ITOH;Minoru Itoh;Minoru Itoh;Minoru Itoh;Minoru Itoh
• 通讯作者: Minoru Itoh

直交Lie 環の冪零元の共軛性について

正交李环幂零元的联合性

• 发表时间: 2012
• 作者: M. Enomoto;T. Ishiwata;綿谷安男;梅田亨;Tetsuya Ishiwata;梅田亨
• 通讯作者: 梅田亨