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Representations whose minimal reduction has a toric identity component


Authors: Claudio Gorodski and Alexander Lytchak
Journal: Proc. Amer. Math. Soc. 143 (2015), 379-386
MSC (2010): Primary 53C40, 20G05
DOI: https://doi.org/10.1090/S0002-9939-2014-12259-3
Published electronically: September 25, 2014
MathSciNet review: 3272762
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Abstract: We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of a (positive-dimensional) toric group. They turn out to be exactly the non-polar irreducible representations preserving an isoparametric submanifold and acting with cohomogeneity one on it.


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Claudio Gorodski
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP 05508-090, Brazil
Email: gorodski@ime.usp.br

Alexander Lytchak
Affiliation: Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany
Email: alytchak@math.uni-koeln.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12259-3
Received by editor(s): March 14, 2013
Published electronically: September 25, 2014
Additional Notes: The first author was partially supported by CNPq grant No. 302472/2009-6 and the FAPESP project 2011/21362-2.
The second author was partially supported by a Heisenberg grant of the DFG and by the SFB 878 Groups, geometry and actions
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2014 American Mathematical Society