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Solution of Broue's conjecture in representation theory of finite groups

有限群表示论中布劳猜想的解

基本信息

批准号：
17540010
负责人：
KOSHITANI Shigeo
金额：
$ 2.45万
依托单位：
Chiba University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540010/
关键词：
finite group representation theory modular representation theory block abelian defect group Broue's conjecture Morita equivalence irreducible character 可挽不足群導来同値

项目摘要

The head investigator Shigeo Koshitani has gotten the following results in the last three yeas.Firstly, Koshitani worked with Morton E.Harris (University of Illinois at Chicago, and we proved that there is a Morita equivalence between two block algebras, say A and B such that A and B are corresponding via the Glauberman corresondence and moreover, the Morita equivalence is described explicitly by an (A,B)-bimodule M which induces the original Glauberman correspondence at the level of ordinary characters. This result has been published in the Journal of Algebra (Elsevier).Secondly, Koshitani has been working with Naoko Kunugi and Katsushi Waki together, in order to solved Broue's abelian defect group conjecture for the fourth Janko simple group J4. This group J4 is relatively quite large in the twenty-six sporadic simple groups. The three people above proved that Broue's abelian defect group conjecture is true for the group J4 for all prime numbers. This result was published in the Jour … More nal of Pure and Applied Algebra (Elsevier). Koshitani has been working on also another kind of Broue's conjecture. Namely, he has been looking at blocks of finite groups whose defect groups are not abelian but metacyclic groups. He with other two co-researchers has gotten some results on the subject as well.The head investigator Shigeo Koshiani announced and gave talks on the above results in many places. Such as at the Mathematical Institute of Oberwolfach, Germany (2006), the Mathematics Luminy Institute, France (2007),University of Chicago, Mathematical Institute of the University of Oxford, University of Aberdeen in the UK, University of Leeds in the UK, University of Jena, Germany, University of Braunsweich Technology, Germany, National University of Ireland in Maynooth, Kyoto University, and so on.On the other hand, Naoko Kunugi, who has been one of the investigators of this project also gave several invited talks on Broue's abelian defect group conjecture. For instance, she gave two talks in the Symposium on algebraic groups and quantum groups held in May 2006 near Nagoya, Japan, and also she gave an invited special talk at the annual meeting orthorized by the Mathematical Society of Japan in September 2006 in Osaka City University. Less

首席调查员Shigeo Koshitani在过去的三年里得到了以下结果。首先，Koshitani与Morton E.Harris合作（University of Illinois at芝加哥，我们证明了两个块代数A和B之间存在Morita等价，使得A和B通过Glauberman对应而对应，而且，Morita等价由（A，B）显式描述。B）-双模M，它在普通特征标的水平上导出了原来的Glauberman对应。该结果已发表在Journal of Algebra（Elsevier）上。其次，Koshitani与Naoko Kunugi和Katsushi Waki一起解决了第四个Janko单群J 4的Broue交换亏群猜想。这个群J 4在26个散在的简单群中是相当大的。上面三个人证明了Broue的交换亏群猜想对群J 4对所有素数都成立。这一结果发表在《Journal》上 ...更多信息《纯粹与应用代数》（Pure and Applied Algebra）小谷一直在研究另一种布鲁猜想。也就是说，他一直在寻找块有限群的缺陷群不是阿贝尔，但亚循环群。他和其他两名合作研究人员也取得了一些成果。首席研究员Shigeo Koshiani在许多地方宣布并发表了关于上述结果的演讲。如在德国奥伯沃尔法赫数学研究所（2006年）、法国卢米尼数学研究所（2007年）、芝加哥大学、牛津大学数学研究所、英国阿伯丁大学、英国利兹大学、德国耶拿大学、德国布劳恩斯维奇理工大学、位于梅努斯的爱尔兰国立大学、京都大学、另一方面，作为该项目的研究者之一的国木直子也就Broue的交换亏群猜想做了几次特邀演讲。例如，她在2006年5月在日本名古屋附近举行的代数群和量子群研讨会上发表了两次演讲，并在2006年9月在大坂市立大学举行的日本数学学会授权的年会上发表了特邀特别演讲。少

项目成果

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Calculations for Broue's abelian defect group conjecture

Broue 阿贝尔缺陷群猜想的计算

DOI：
发表时间：
2006
期刊：
数理解析研究所講究録 1466
影响因子：
0
作者：
Morton E.Harris;Shigeo Koshitani;Shigeo Koshitani;Shigeo Koshitani
通讯作者：
Shigeo Koshitani

Broue's abelian defect group conjecture

布劳的阿贝尔缺陷群猜想

DOI：
发表时间：
2014
期刊：
影响因子：
0
作者：
R.Kessar;S.Koshitani;M.Linckelmann;S. Koshitani;S. Koshitani;S. Koshitani;S. Koshitani;S. Koshitani;S. Koshitani
通讯作者：
S. Koshitani

An extension of Watanabe's theorem for the Isaacs-Horimoto-Watanabe

Isaacs-Horimoto-Watanabe 渡边定理的扩展