| Project/Area Number |
23540026
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Sophia University |
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Principal Investigator |
Gomi Yasushi 上智大学, 理工学部, 准教授 (50276515)
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| 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)
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| Research Collaborator |
Ma. Louise Antonette N. De Las Penas Ateneo de Manila University
Loyola Mark L. Ateneo de Manila University
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| 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 |
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| 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.
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