manuscripta mathematica

, Volume 104, Issue 3, pp 309–324 | Cite as

Reducible polar representations

  • Isabel Bergmann


In this paper the reducible polar representations of the compact connected Lie groups are classified. It turns out that there only exist “interesting” reducible polar representations of Lie groups of the types A 3, A 3×T 1, B 3, B 3×T 1, D 4, D 4×T 1 and D 4×A 1. Up to equivalence, there is just one such representation of the first four Lie groups, there are three reducible polar representations of D 4 and six of D 4×T 1 and D 4×A 1, respectively. From this follows immediately the classification of the compact connected subgroups of SO(n) which act transitively on products of spheres.

Mathematics Subject Classification (2000): 22E46, 53C35 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Isabel Bergmann
    • 1
  1. 1.Institut für Mathematik, Universität Augsburg, 86153 Augsburg, Germany. e-mail: isabel.bergmann@math.uni-augsburg.deDE

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