On orbit spaces of representations of compact Lie groups

Author(s)

Gorodski, Claudio ^[1] ; Lytchak, Alexander ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, BR-05508090 Sao Paulo - Brazil

^[2] Univ Cologne, Math Inst, D-50931 Cologne - Germany

• Document type: Journal article
• Source: JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK; v. 691, p. 61-100, JUN 2014.
• Web of Science Citations: 12

Abstract

We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and investigate properties of the corresponding representations. We obtain some structural results and apply them to study irreducible representations of small copolarity. As an important tool, we classify all irreducible representations of connected groups with cohomogeneity four or five. (AU)

• FAPESP's process: 07/03192-7 - Submanifold geometry and Morse theory in finite and infinite dimensions
• Grantee: Claudio Gorodski
• Support Opportunities: Research Projects - Thematic Grants