Research on a classification theory of prehomogeneous vector spaces
Project/Area Number |
22540009
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | University of Tsukuba |
Principal Investigator |
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Project Period (FY) |
2010 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | 群の表現論 / 概均質ベクトル空間 / 分類 / 普遍推移性 / 有限個の軌道 / 重み付きクイバー / 傾加群 |
Research Abstract |
The basic theory of prehomogeneous vector spaces was first obtained by Mikio Sato, and later many mathematicians have been developing this theory. This has been investigated by number theoretical method, algebra-analytic methos or representation theoretical method. There are applications to the theory of zeta functions etc. Hence it is an important problem to classify them to know what kind of examples exist.The first result was a classification of irreducible prehomogeneous vector spaces obtained by Mikio Sato and Tatsuo Kimura. However a classification problem is very difficult and some mathematicians say impossible. But Mikio Sato has some result even for non-irreducible case. In our work, we developed a lot his results. We have also classified some prehomogeneous vector spaces with the different view point from M. Sato’s research. We also find some tools such as PV-equivalences.
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Report
(4 results)
Research Products
(10 results)