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Abstract

Let G be the Lie group SO(n, ‫)ޒ‬ × SO(n, ‫)ޒ‬ and let V be the vector space of n × n real matrices. An action of G on V is given byWe consider the orbits of this group action and demonstrate a cross-section to the orbits. We then determine the stabilizer for a typical element in this crosssection and completely describe the fundamental group of an orbit of maximal dimension.