Representation theory of Iwahori-Hecke algebras and reflection groups

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540026
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Sophia University
• Principal Investigator: Gomi Yasushi 上智大学, 理工学部, 准教授 (50276515)
• Co-Investigator(Kenkyū-buntansha): NAKASHIMA Toshiki 上智大学, 理工学部, 教授 (60243193) ; SHINODA Ken-ichi 上智大学, 理工学部, 教授 (20053712)
• Research Collaborator: Ma. Louise Antonette N. De Las Penas Ateneo de Manila University ; Loyola Mark L. Ateneo de Manila University
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 岩堀ヘッケ環 / マルコフトレース / 鏡映群 / ガウス和 / ストリングC群

Outline of Final Research Achievements

I studied q-analogues of Gauss sums on finite Coxeter groups which are generalization of classical Gauss sums. Then I gave the definition of Gauss sums on the Iwahori-Hecke algebras of type A and determined the values. Furthermore, I found that the corresponding trace functions on Iwahori-Hecke algebras are closely related to the Markov trace, and determined the values of the trace functions.
In addition, I studied the classification of string C-groups which are generalization of Coxeter groups. I focused into 2-groups, and I proved that in case of rank 3, all string C-groups are obtained as central extensions of string C-groups by 2. Using this theorem, I determined all string C-groups of order 1024.

Free Research Field

代数学