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

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540007
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba University
• Principal Investigator: KOSHITANI Shigeo 千葉大学, 理学(系)研究科(研究院), 教授 (30125926)
• Co-Investigator(Renkei-kenkyūsha): KUNUGI Naoko 東京理科大学, 理学部第一部, 准教授 (50362306)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: ブルエ予想 / 表現論 / 有限群 / ブロック / 森田同値 / 導来同値 / アルペリン予想 / マッカイ予想

Outline of Final Research Achievements

For the subject "Broue's conjecture", we have been able to prove the following. First of all, we proved Broue's conjecture for the sproradic simple Conway group Co3 completely. Then, we prove Broue's conjecture of character version for an arbitrary block with elementary abelian defect group of order 8. This was the first improvement after Brauer did 35 years ago. Further, we proved Broue's conjecture for the sporadic Janko simple group J4 more precisely. We proved Broue's conjecture also for the double cover 2HS of the sporadic Higman-Sims simple group HS. Finally we proved Broue's conjecture for the sporadic Conway simple group Co1, and as a byproduct we could determine the 3-decomposition numbers for Co1 in part.

Free Research Field

数物系科学, 科研費の分科細目：数学、代数学