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Journal of Lie Theory 27 (2017), No. 3, 801--829
Copyright Heldermann Verlag 2017

Maximal Antipodal Subgroups of some Compact Classical Lie Groups

Makiko Sumi Tanaka
Dept. of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan

Hiroyuki Tasaki
Division of Mathematics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

We classify maximal antipodal subgroups of the quotient groups of the compact classical Lie groups and explicitly describe them by using the dihedral group of order 8. The maximal antipodal subgroups are not unique up to conjugation in almost all cases.

Keywords: Antipodal subgroup, compact Lie group, polar.

MSC: 22E40, 53C35

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