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
tanaka_makiko@ma.noda.tus.ac.jp
Hiroyuki Tasaki
Division of Mathematics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
tasaki@math.tsukuba.ac.jp
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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