Involve: A Journal of Mathematics

  • Involve
  • Volume 2, Number 5 (2009), 495-509.

On the orbits of an orthogonal group action

Kyle Czarnecki, R. Michael Howe, and Aaron McTavish

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Let G be the Lie group SO(n,)× SO(n,) and let V be the vector space of n×n real matrices. An action of G on V is given by

( g , h ) . v : = g 1 v h , ( g , h ) G , v V .

We 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 cross-section and completely describe the fundamental group of an orbit of maximal dimension.

Article information

Involve, Volume 2, Number 5 (2009), 495-509.

Received: 8 April 2008
Accepted: 28 September 2009
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22C05: Compact groups 57S15: Compact Lie groups of differentiable transformations
Secondary: 55Q52: Homotopy groups of special spaces

representation theory orbit Lie group homotopy group Clifford algebra


Czarnecki, Kyle; Howe, R. Michael; McTavish, Aaron. On the orbits of an orthogonal group action. Involve 2 (2009), no. 5, 495--509. doi:10.2140/involve.2009.2.495.

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