Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogeneous spherical data of orbits in spherical embeddings   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
$G/H \hookrightarrow X$. As an application, we obtain a description of the
colored fan associated to the spherical embedding $X_0 \hookrightarrow
\bar{X_0}$.

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The categories of this paper are: supr-con
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex