Algebraic structure and geometric harmonic analysis of homogeneous open convex cones and homogeneous real Siegel domains

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540177
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: NOMURA Takaaki 九州大学, 数理(科)学研究科(研究院), 教授 (30135511)
• Co-Investigator(Renkei-kenkyūsha): ISHI Hideyuki (00326268)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 等質開凸錐 / 等質ジーゲル領域 / 基本相対不変式 / 非結合的代数 / 左対称代数 / 向き付けグラフ / 正定値対称行列

Outline of Final Research Achievements

Cones which are both open and convex sets in Euclidean spaces are called open convex cones. Open convex cones on which Lie groups act transitively are said to be homogeneous. Domains that appear as sections of homogeneous convex cones by hyperplanes not passing through the origin are called homogeneous real Siegel domains. In this research, we have investigated their various structures, in particular, we have described explicit formulae of basic relative invariants which have intimate relations with the algebraic structure, and have obtained realizations of general open convex cones through oriented graphs.

Free Research Field

非可換調和解析