Quantization of singular nilpotent orbits of reductive Lie groups and realization of unitary representations

Research Project

Project/Area Number	25400103
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Basic analysis
Research Institution	Hokkaido University
Principal Investigator	Yamashita Hiroshi 北海道大学, 理学研究院, 教授 (30192793)
Co-Investigator(Renkei-kenkyūsha)	SAITO Mutsumi 北海道大学, 大学院理学研究院, 教授 (70215565) ABE Noriyuki 北海道大学, 大学院理学研究院, 准教授 (00553629)
Project Period (FY)	2013-04-01 – 2017-03-31
Project Status	Completed (Fiscal Year 2016)
Budget Amount *help	¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000) Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000) Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000) Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords	リー群のユニタリ表現
Outline of Final Research Achievements	In this research project, we aimed to give a good realization of irreducible unitary representations of reductive Lie groups corresponding to singular nilpotent orbits through geometric quantization of adjoint orbits. As a result, the embeddings of every singular quaternionic unitary representation of exceptional simple Lie groups of real rank 4 into real parabolically induced modules (the principal series) are specified, and we have shown the uniqueness of such embeddings. Moreover, geometric structure of singular quaternionic nilpotent orbits has been described in terms of lower rank Hermite symmetric pairs (tube type) or quaternionic symmetric pairs.