Clarification, extension and application of antipodal sets of symmetric spaces

2020 Fiscal Year Final Research Report

• Project/Area Number: 18K03268
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11020:Geometry-related
• Research Institution: University of Tsukuba
• Principal Investigator: Tasaki Hiroyuki 筑波大学, 数理物質系, 准教授 (30179684)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Keywords: 対称空間 / 対蹠集合 / 実形の交叉 / 複素旗多様体 / 有向実Grassmann多様体

Outline of Final Research Achievements

We explicitly describe the classifications of maximal antipodal sets in compact symmetric spaces of classical type which can be realized as polars of connected compact Lie groups. Even in the case where a compact symmetric space cannot be realized as a polar of a connected compact Lie group, it can be realized as a polar of a disconnected compact Lie group and we classify maximal antipodal subgroups in a disconnected compact Lie group and we proceeded with the research on classifications of maximal antipodal sets in polars. In many cases the classifications of maximal antipodal sets have been completed.

Free Research Field

微分幾何学

Academic Significance and Societal Importance of the Research Achievements

連結コンパクトLie群の極地として実現できないコンパクト対称空間を非連結コンパクトLie群の極地として実現することにより、コンパクト対称空間の極大対蹠集合を詳しく調べる手法を確立したことは、極大対蹠集合の分類に役立っただけではなく、極大対蹠集合の幾何学的、代数的、組合せ論的性質を調べる上でも有用である。このように非連結コンパクトLie群の極地を解明することは学術的意義がある。