Combinatorial characterization of the weight monoids of smooth affine spherical varieties

Pezzini, Guido; Van Steirteghem, Bart

doi:10.1090/tran/7785

Combinatorial characterization of the weight monoids of smooth affine spherical varieties

Authors: Guido Pezzini and Bart Van Steirteghem
Journal: Trans. Amer. Math. Soc. 372 (2019), 2875-2919
MSC (2010): Primary 14M27, 20G05
DOI: https://doi.org/10.1090/tran/7785
Published electronically: February 25, 2019
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Abstract: Let be a connected reductive group, and let be a smooth affine spherical -variety, both defined over the complex numbers. A well-known theorem of I. Losev's says that is uniquely determined by its weight monoid, which is the set of irreducible representations of that occur in the coordinate ring of . In this paper, we use the combinatorial theory of spherical varieties and a smoothness criterion of R. Camus to characterize the weight monoids of smooth affine spherical varieties.

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