2009 Fiscal Year Final Research Report
Geometric Harmonic Analysis on Homogeneous Cones and Homogeneous Siegel Domains
| Project/Area Number |
18340039
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
NOMURA Takaaki Kyushu University, 大学院・数理学研究院, 教授 (30135511)
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| Co-Investigator(Kenkyū-buntansha) |
WAKAYAMA Masato 九州大学, 大学院・数理学研究院, 教授 (40201149)
FUJIWARA Hidenori 近畿大学, 産業理工学部, 教授 (50108643)
UMEDA Toru 京都大学, 大学院・理学研究科, 准教授 (00176728)
ITOH Minoru 鹿児島大学, 理学部, 准教授 (60381141)
ISHI Hideyuki 名古屋大学, 大学院・多元数理科学研究科, 准教授 (00326068)
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| Co-Investigator(Renkei-kenkyūsha) |
KAI Chifune 金沢大学, 大学院・自然科学研究科, 助教 (70506815)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 解析学 / 関数解析学 / 関数論 / 幾何学 / ジーゲル領域 / 等質錐 / ジョルダン代数 |
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| Research Abstract |
There has been a conjecture concerning the gaps between the degrees of the basic relative invariants associated to homogeneous cones and the symmetry of the corresponding homogeneous tube domains (Siegel domains of the first kind).However, we found a homogeneous cone that denies the conjecture. Moreover such a cone is found in any rank greater than or equal to 3. We also discovered a homogeneous cone of arbitrary rank greater than or equal to 3 that is linearly isomorphic to its dual cone. Further, we proved that the basic relative invariants are exactly the irreducible factors of the determinant of the right multiplication operators in the complexification of the clan corresponding to the cone. In the case of symmetric cone, we computed an actual decomposition of that determinant into irreducible factors.
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