Zeta functions pf prehomogeneous vector spaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 24340001
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Yukie Akihiko 京都大学, 理学(系)研究科(研究院), 教授 (20312548)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 概均質ベクトル空間 / 有理軌道 / 局所ゼータ関数 / 密度定理

Outline of Final Research Achievements

We were aiming at determining determining orbits over the p-adic integer ring. For that purpose, we considered representations of reductive groups which are not necessarily split over a complete field. We proved that the stratification and the inductive structure of the set of unstable points is rational over the ground field. Also we came up with an arithmetic interpretation of rational orbits of the space of paris of exceptional Jordan algebras. When the corresponding octonion is split, we proved that rational orbits correspond bijectively with cubic extensions of the ground field. Also we constructed the equivariant map of the lowest degree which is associated with this representation.

Free Research Field

整数論