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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