Representations whose minimal reduction has a toric identity component

2012/12/22 by Gorodski, Claudio, Lytchak, Alexander
#20G05 #53C40 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1212.5706

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 (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.

Related

• Representations with Sp(1)^k-reductions and quaternion-Kähler symmetric spaces
• Representations of low copolarity
• On orbit spaces of representations of compact Lie groups
• Representations of compact simple Lie groups whose orbit space has non-empty boundary
• Representations of compact Lie groups and the osculating spaces of their orbits