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Dimension Formula for Slice for Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras

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Geometric and Harmonic Analysis on Homogeneous Spaces and Applications (TJC 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 207))

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Abstract

The recent paper [19] has studied spherical nilpotent orbits in complex simple Lie algebras from the viewpoint of the notion of strongly visible actions introduced by T. Kobayashi. The aim of this paper is to give a dimension formula for a slice for the strongly visible action on a spherical nilpotent orbit. This provides an unified explanation of the strong visibility for the action on a spherical nilpotent orbit. Further, we prove that our choice of slice for this action satisfies its dimension equals the rank of a nilpotent orbit, which suggests a deep relation between complex geometry and multiplicity-free representation in complex nilpotent orbits.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Tokai University, 4-1-1, Kitakaname, Hiratsuka, Kanagawa, 259-1292, Japan

    Atsumu Sasaki

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  1. Atsumu Sasaki
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Correspondence to Atsumu Sasaki .

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Editors and Affiliations

  1. Département de Mathématiques, Université de Sfax, Sfax, Tunisia

    Ali Baklouti

  2. Faculty of Mathematics, Kyushu University, Fukuoka, Fukuoka, Japan

    Takaaki Nomura

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Sasaki, A. (2017). Dimension Formula for Slice for Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras. In: Baklouti, A., Nomura, T. (eds) Geometric and Harmonic Analysis on Homogeneous Spaces and Applications. TJC 2015. Springer Proceedings in Mathematics & Statistics, vol 207. Springer, Cham. https://doi.org/10.1007/978-3-319-65181-1_8

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