2012 Fiscal Year Final Research Report
Representation of finite groups, character sums, and their applications
| Project/Area Number |
21540024
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
NAKASHIMA Toshiki 上智大学, 理工学部, 教授 (60243193)
GOMI Yasushi 上智大学, 理工学部, 准教授 (50276515)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 有限群の表現論 / ガウス和 / 指標和 |
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| Research Abstract |
Gauss sum, which depends on a prime p, was considered by F. Gauss about 200 years ago and he determined the value beautifully. Since the sum is over 0 to p-1, it can be regarded as a sum over a finite prime field. There has been many works which extend the results. In this research, we defined a Gauss sum for arbitrary finite groups, and determined its value explicitly, particularly for basic finite groups, like symmetric groups and some complex reflection groups
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