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在最后三个Yeas中获得了以下结果。首先，Koshitani与Morton E.Harris（伊利诺伊州伊利诺伊大学的芝加哥大学合作），我们规定，两个块代数在A和B之间存在莫里塔的等效性，例如，A和B之间的Elexentive a和B Glauberman的对应关系以及MORIA的相当性，并且是Morea，Morea and Morea and oi a。（a，b）诱导普通字符级别的原始glauberman对应。在二十六个零星的小组中，大型的三人证明，Broue的Abelian缺陷组概念对于所有素数来说都是如此。科希塔尼（Koshitani）也一直在研究另一种布鲁伊（Broue）的概念。也就是说，他一直在寻找有限群体的群体，这些有限群体的缺陷群体不是阿贝利安，而是梅西克利组。他与其他两位共同研究者也对该主题取得了一些成果。调查员Shigeo Koshiani宣布，并在许多地方就上述结果进行了会谈。例如在德国奥伯瓦尔省数学研究所（2006年），法国数学Luminy Institute（2007年），芝加哥大学，牛津数学研究所，牛津大学，英国阿伯丁大学，英国的利兹大学，英国，德国，德国大学，德国大学，布拉拉斯瓦奇大学，梅斯瓦奇大学，国民大学。另一方面，曾是该项目的调查人员之一的Naoko Kunugi也对Broue的Abelian缺陷小组概念进行了几次邀请的演讲。例如，她在2006年5月在日本纳戈亚（Nagoya）举行的代数团体和量子群的研讨会上进行了两次演讲，她在2006年9月在大阪市大学的日本数学学会矫正会上进行了特别的特别演讲。较少的

项目成果

期刊论文数量（0）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

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

The indecomposability of a certain bimodule given by the Brauer construction

布劳尔构造给出的某个双模的不可分解性

DOI：
发表时间：
2005
期刊：
Journal of Algebra 285
影响因子：
0
作者：
Shigeo Koshitani;Markus Linckelmann
通讯作者：
Markus Linckelmann

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

Isaacs-Horimoto-Watanabe 渡边定理的扩展

DOI：
发表时间：
2006
期刊：
Journal of Algebra 296
影响因子：
0
作者：
Morton E.Harris;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

Trivial source modules in blocks with cyclic defect groups

具有循环缺陷组的块中的简单源模块