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

Claudio Gorodski; Francisco J. Gozzi

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

Differential Geometry 2017-02-27 v1 Metric Geometry Representation Theory

Authors: Claudio Gorodski , Francisco J. Gozzi

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".

Keywords

Sp(1)^k-reductions quaternion-Kahler symmetric spaces non-polar irreducible representations orbit space isotropy representations

Cite

@article{arxiv.1702.07695,
  title  = {Representations with $Sp(1)^k$-reductions and quaternion-K\"ahler symmetric spaces},
  author = {Claudio Gorodski and Francisco J. Gozzi},
  journal= {arXiv preprint arXiv:1702.07695},
  year   = {2017}
}

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10 pages

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

Abstract

Keywords

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