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

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".

10 pages

References in corpus (1)

• Homogeneity rank of real representations of compact Lie groups