Representations with $Sp(1)^k$-reductions and quaternion-K\"ahler symmetric spaces

Claudio Gorodski; Francisco J. Gozzi

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arXiv · 1702.07695

Representations with $Sp(1)^k$-reductions and quaternion-K\"ahler symmetric spaces

Claudio Gorodski·Francisco J. Gozzi

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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-K\"ahler symmetric spaces by restricting to the "non-$Sp(1)$-factor".

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BibTeX RIS

Claudio Gorodski, Francisco J. Gozzi. 2017-02-24. Representations with $Sp(1)^k$-reductions and quaternion-K\"ahler symmetric spaces. https://arxiv.org/abs/1702.07695

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