Abstract:
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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 28 April 2000
Rights and permissions
About this article
Cite this article
Bergmann, I. Reducible polar representations. manuscripta math. 104, 309–324 (2001). https://doi.org/10.1007/s002290170029
Issue Date:
DOI: https://doi.org/10.1007/s002290170029