Classification and representation theoretic study of the functional equation-spaces
Project/Area Number |
20540021
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Josai University |
Principal Investigator |
|
Co-Investigator(Renkei-kenkyūsha) |
SATO Fumihiro 立教大学, 理学部, 教授 (20120884)
|
Project Period (FY) |
2008 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | 代数学一般 / 表現論 / 局所関数等式 / 概均質ベクトル空間 / Clifford代数の表現 / 2次写像 / 2次形式 / Lie群 / スピン表現 / clifford代数の表現 / Clifford-Klein form / Hurwitz-Radon number / Clifford-Klien form / Hurwitz-Radon数 / Hopf fibration / 2次球写像 / Orthogonal designs / 関数等式のpull back / 自己双対非退化2次写像 / Spin群 / 不変多項式 |
Research Abstract |
Let Cp(resp. Cq) be the Clifford algebra of a positive definite real quadratic form in p(resp. q) variables. For a representationρof the tensor product of Cp and Cq, we can associate a homogeneous polynomial P of degree 4 on the representation space ofρhaving the property "The Fourier transform of the complex power}}| P|^s coincides with|P*|^{-m/4-s}(m=the degree ofρ) with an explicit gamma factor. Owing to the theory of prehomogeneous vector spaces, the basic relative invariant of an irreducible regular prehomogeneous vector space satisfies the property above. However the polynomials P are not necessarily relative invariants of any prehomogeneous vector spaces. The polynomials P are relative invariants of prehomogeneous vector spaces only for quite few exceptional cases. In this study, we discuss the structure and the action of the group of linear transformations that leave P invariant.
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Report
(6 results)
Research Products
(49 results)