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Study of generating functions viewed from group theory and category theory

从群论和范畴论角度研究生成函数

基本信息

批准号：
13440001
负责人：
YOSHIDA Tomoyuki
金额：
$ 8.19万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440001/
关键词：
The number of group homomorphisms Cohomol of groups Topos Mackev functor Burnside ring Exponential formula Modular representation 有限群の準同形写像符号の重み多項式有限群のモジュラー表現母関数プレシズム丹原関手

项目摘要

1.Asai-Yoshida's conjecture on the number of group homomorphisms has a connection with p-adic anallysis (Yoshida, Takegahara, K.Conrad, etc.). Furthermore, Yoshida solved the conjecture for the homomorphisms from the fundamental group of a compact Riemann surface whose importence in quantum field theory was pointed by M.Mulase.2.Yoshida and Oda accomplished a fundamental theory of crossed Burnside rings of finite groups.3.Yoshida, Sasaki, Oda study cohomology theory of finite groups, especially Hochschild cohomology, crossed Mackey functors and quantum doubles of group algebra.4.Yoshida, Bannai and Keisuke Shiromoto sutudies combinatorics, in particular, distance regular graphs, designs and code theory, especially an application of homological algebra to the theory of codes on a ring.5.Koshitani studies modular representation thoery of finite groups and gave an affirmative answer to the Broue conjecture for groups with some special defect groups.6.Nakamura and Yamashita studied some related areas (algebraic geometry and representation theory) and gave some interested results, especially a relation with finite simple groups.7.We invited three mathematicians from abroad.・2001 FAN Yun(Wuhan U.) Talk on Broue conjecture(Kyushu Univ.)・2003 Keith CONRAD(Connecticut U.) Talk of p-adic analysis, number theory(Hokkaido U., Kyoto U.)・2004 Segre BOUC(CNRS) Talk on Dade groups and Burnside rings (Hokaido U., Kyoto U.)A large number of results of this research has been printed and published. The remainder results will be serially published. The investigator gave some talks related to this research in some conferences--"Generating functions and related topics" (Sapporo 2001), "20-th Symposium on Algebraic Combinatorics (Kyoto 2002), "Extended Group Seminar" (Sapporo 2002,2004, and so on.

1.Asai-Yoshida关于群同态个数的猜想与P-adic分析（Yoshida，Takegahara，K.Conrad等）有关。M. Mulase指出紧致Riemann曲面的基本群的同态猜想在量子场论中的重要性。2. Yoshida和Oda完成了有限群的交叉伯恩赛德环的基本理论。3. Yoshida，Sasaki和Oda研究了有限群的上同调理论，特别是Hochschild上同调，交叉Mackey函子和群代数的量子双。Bannai和Keisuke Shiromoto研究组合学，特别是距离正则图，设计和代码理论，5. Koshitani研究了有限群的模表示理论，并对具有某些特殊亏群的群的Broue猜想给出了肯定的回答（代数几何与表示论），并给出了一些有趣的结果，特别是与有限单群的关系。7.我们邀请了三位国外数学家。2001范云（武汉大学）Broue猜想讲座（九州大学）·2003年基思康拉德（康涅狄格大学）谈p-adic分析、数论（北海道大学，京都大学）·2004年塞格雷BOUC（CNRS）关于Dade群和伯恩赛德环的讲座（北海道大学，京都大学）这项研究的大量成果已被印刷和出版。其余结果将连续公布。研究者在一些会议上发表了一些与本研究相关的演讲--“生成函数和相关主题”（札幌2001）、“第20届代数组合学研讨会”（京都2002）、“扩展小组研讨会”（札幌2002、2004）等。