Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some families of smooth affine spherical varieties of full rank   Let G be a complex connected reductive group. I. Losev has shown that a
smooth affine spherical G-variety X is uniquely determined by its weight
monoid, which is the set of irreducible representations of G that occur in the
coordinate ring of X. In this paper we use a combinatorial characterization of
the weight monoids of smooth affine spherical varieties to classify: (a) all
such varieties when G is $\mathrm{SL}(2) \times \mathbb{C}^{\times}$ and (b)
all such varieties for G simple which have a G-saturated weight monoid of full
rank. We also use the characterization and F. Knop's classification theorem for
multiplicity free Hamiltonian manifolds to give a new proof of C. Woodward's
result that every reflective Delzant polytope is the moment polytope of such a
manifold.

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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas