A COMPLETE DESCRIPTION OF THE ANTIPODAL SET OF MOST SYMMETRIC SPACES OF COMPACT TYPE

Beyrer, Jonas

doi:https://doi.org/10.18910/70088

アクセス数:81件（2024-12-12 10:40 集計）

固定URL: https://doi.org/10.18910/70088

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タイトル	A COMPLETE DESCRIPTION OF THE ANTIPODAL SET OF MOST SYMMETRIC SPACES OF COMPACT TYPE
著者	著者名 Beyrer, Jonas
抄録	It is known that the antipodal set of a Riemannian symmetric space of compact type G/K consists of a union of K-orbits. We determine the dimensions of these K-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we are not going to deal with are those with restricted root system a_r and a non-trivial fundamental group, which is not isomorphic to ℤ_2 or ℤ_<r+1>. For example, we show that the antipodal sets of the Lie groups Spin(2r + 1) r ≥ 5, E_8 and G_2 consist only of one orbit which is of dimension 2r, 128 and 6, respectively; SO(2r + 1) has also an antipodal set of dimension 2r; and the Grassmannian Gr_<r,r+q>(ℝ) has a rq-dimensional orbit as antipodal set if r ≥ 5 and r≠q > 0.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	55(3)
ページ	567-586
刊行年月	2018-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/70088
DOI	https://doi.org/10.18910/70088
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 55, Number 3 （2018-7）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2018, 55(3), p. 567-586
DC.title	A COMPLETE DESCRIPTION OF THE ANTIPODAL SET OF MOST SYMMETRIC SPACES OF COMPACT TYPE
DC.creator	Beyrer, Jonas
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2018-07
DCTERMS.abstract	It is known that the antipodal set of a Riemannian symmetric space of compact type G/K consists of a union of K-orbits. We determine the dimensions of these K-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we are not going to deal with are those with restricted root system a_r and a non-trivial fundamental group, which is not isomorphic to ℤ_2 or ℤ_<r+1>. For example, we show that the antipodal sets of the Lie groups Spin(2r + 1) r ≥ 5, E_8 and G_2 consist only of one orbit which is of dimension 2r, 128 and 6, respectively; SO(2r + 1) has also an antipodal set of dimension 2r; and the Grassmannian Gr_<r,r+q>(ℝ) has a rq-dimensional orbit as antipodal set if r ≥ 5 and r≠q > 0.
DC.identifier	10.18910/70088
DC.format	70088
citation_title	A COMPLETE DESCRIPTION OF THE ANTIPODAL SET OF MOST SYMMETRIC SPACES OF COMPACT TYPE
citation_author	Beyrer, Jonas
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2018-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	55
citation_issue	3
citation_firstpage	567
citation_lastpage	586
citation_public_url	https://hdl.handle.net/11094/70088
citation_doi_detail	10.18910/70088
citation_doi	https://doi.org/10.18910/70088

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