A complete description of the antipodal set of most symmetric spaces of compact type

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 \mathfrak a_r and a non-trivial fundamental group, which is not isomorphic to \mathbb Z_2 or \mathbb 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.

SEEK ID: https://publications.h-its.org/publications/988

Research Groups: Groups and Geometry

Publication type: Journal

Journal: Osaka J. Math

Citation: Osaka J. Math 55(3):567–586

Date Published: 2018

URL: https://projecteuclid.org/euclid.ojm/1530691244

Registered Mode: imported from a bibtex file

Author: Jonas Beyrer

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Created: 30th Jan 2020 at 10:21

Last updated: 5th Mar 2024 at 21:24

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