
Journal of Lie Theory 27 (2017), No. 3, 801829 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 2788510, Japan tanaka_makiko@ma.noda.tus.ac.jp Hiroyuki Tasaki Division of Mathematics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 3058571, 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 [ Fulltextpdf (324 KB)] for subscribers only. 