一般合流超幾何関数の研究

一般汇合超几何函数的研究

• 批准号: 05229002
• 负责人: 木村 弘信
• 金额: $ 0.77万
• 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 on Priority Areas
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05229002/
• 关键词: 超幾何関数; 合流; 隣接関係式; ハミルトニアン

この研究の目的は古典的に知られている超幾何関数および合流型超幾何関数を含む多変数超幾何関数の理論を建設することである.当該年度の研究目的は具体的には次の2点であった.(1)合流型超幾何関数の付随するtwisted cohomology,twisted homologyの理論の整備(2)合流型超幾何関数の隣接関係式とToda latticeの関係の解明.上記の目的についての研究成果は次のとおりである.(1)について.合流型超幾何関数が1重積分で表される場合には,積分に意味を与えるhomologyはfamily of supportsを持つtwisted homologyで記述されるが,homologyの代表元を与えるcycleを具体的に構成することができた.またcohomologyについては,rational twisted de Rham cohomologyを具体的に計算した.更に,多重積分で与えられるAiry関数の場合には,付随するrational de Rham cohomologyについて,特異点理論における孤立特異点に関する結果を用いることにより,その消滅と生き残るcohomologyの次元についての結果を得た.(2)について.Toda latticeとの関係は未だに不明であるが,隣接関係式を生成する1階微分作用素の作るLie環に関する結果として,このLie環がGL(n)のLie環の必ずしもsemisimpleでない極大可換部分環に関するroot space分解によって自然に記述されることを明らかにした.

The purpose of this study is to study the classical theory of how to understand the number of confluence type, including the theory of "multi-number" and "how many numbers". In the current year, the specific objectives of the study will be discussed at 2 o'clock. (1) the number of confluence type will be paid along with the theory of twisted cohomology,twisted homology theory. (2) the explanation of confluence type Toda lattice theory. The purpose of this article is to discuss the results of the research. (1) the results of the research. The multiple data table of the confluent type is divided into two parts, which means that the twisted homology is recorded with the homology family of supports, and the homology represents the specific data of the yuan and cycle. This is the specific calculation of cohomology calculation and rational twisted de Rham cohomology calculation. More importantly, the multiple Airy data sets are closely related to each other, and the results are similar to those of the rational de Rham cohomology cluster. The special theory is that the isolated special point results show that the results show that the results are not known. The results show that the results show that the results are not known. (2) the results show that the results are not known. The results show that the results are not known. (2) the results of the results show that the results are not known. (2) the results of the results show that the results are not known. (2) the results show that the results are not known. The results are not known. The first step is to generate a differential action element for the Lie environment. The results show that the Lie environment GL (n) requires a high level of environmental pollution (semisimple). Part of the environment is available. The root space decomposition cycle is a natural record of environmental pollution.

项目成果

H.Kimura,Y.Haraoka,K.Takano: "On confluences of the General hypergeometric Systems" Proc.of the Japan Acad.69. 99-104 (1993)

H.Kimura、Y.Haraoka、K.Takano：“论一般超几何系统的汇合”Proc.of the Japan Acad.69。

Y.Haraoka,H.Kimura: "Contiguity velations of Generalized confluent hypergeomeric functions" Proceedings of the Japan Academy. 69. 105-110 (1993)

Y.Haraoka，H.Kimura：“广义汇合超几何函数的邻接性揭示”日本学士院学报。

H.Kimura,Y.Haraoka,K.Takano: "On Contiguity velations of the confluent hypergeometric systems" Proceedings of the Japan Academy. 70. 47-49 (1994)

H.Kimura、Y.Haraoka、K.Takano：“论汇合超几何系统的连续性揭示”日本学士院学报。

H.Kimura: "Uniform foliation Associated with the Hamiltonicm systems 〓n" Annali della Scuola Normale Saperiore di Pisa.20. 1-60 (1993)

H.Kimura：“与 Hamiltonicm 系统相关的均匀叶状结构〓n”Annali della Scuola Normale Saperiore di Pisa.20 (1993)。