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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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 有限群の表現論 / ガウス和 / 指標和 / 有限群の表現 / 代数 / 有限群 / 表現 / 指標 / 代数学 |
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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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Report
(5 results)
Research Products
(15 results)
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[Presentation] 有限群のガウス和2009
Author(s)
K.Shinoda
Organizer
「ゲーム理論と表現論」研究集会
Place of Presentation
稚内北星学園大学
Year and Date
2009-08-24
Related Report
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