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HOMOGENEOUS SPHERICAL DATA OF ORBITS IN SPHERICAL EMBEDDINGS

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Abstract

Let G be a connected reductive complex algebraic group. Luna assigned to any spherical homogeneous space G/H a combinatorial object called a homogeneous spherical datum. By a theorem of Losev, this object uniquely determines G/H up to G-equivariant isomorphism. In this paper, we determine the homogeneous spherical datum of a G-orbit X 0 in a spherical embedding G/H ↪ X. As an application, we obtain a description of the colored fan associated to the spherical embedding X 0 ↪ \( \overline{X_0} \).

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  1. Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    GIULIANO GAGLIARDI & JOHANNES HOFSCHEIER

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  1. GIULIANO GAGLIARDI
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  2. JOHANNES HOFSCHEIER
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Correspondence to GIULIANO GAGLIARDI.

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GAGLIARDI, G., HOFSCHEIER, J. HOMOGENEOUS SPHERICAL DATA OF ORBITS IN SPHERICAL EMBEDDINGS. Transformation Groups 20, 83–98 (2015). https://doi.org/10.1007/s00031-014-9297-2

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  • DOI: https://doi.org/10.1007/s00031-014-9297-2

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