Representations with Sp(1)^k-reductions and quaternion-Kähler symmetric spaces

2017/02/24 by Cláudio Gorodski, Gorodski, Claudio, Francisco J. Gozzi +1
Mathematics · #22E46 #53C35 #57S15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1702.07695

openalex publication_date 2017/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify non-polar irreducible representations of connected compact Lie groups whose orbit space is isometric to that of a representation of a finite extension of Sp(1)^k for some k>0. It follows that they are obtained from isotropy representations of certain quaternion-Kähler symmetric spaces by restricting to the "non-Sp(1)-factor".

Related

• Representations whose minimal reduction has a toric identity component
• Representations of low copolarity
• On homogeneous manifolds whose isotropy actions are polar
• Integrability of quaternion-Kähler symmetric spaces
• Polar actions on Hermitian and quaternion-Kähler symmetric spaces