COMBINATORIAL CHARACTERIZATION OF THE WEIGHT MONOIDS OF SMOOTH AFFINE SPHERICAL VARIETIES

Pezzini G, van Steirteghem B (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Transactions of the American Mathematical Society American Mathematical Society

Book Volume: 372

Pages Range: 2875-2919

Journal Issue: 4

DOI: 10.1090/tran/7785

Abstract

Let G be a connected reductive group, and let X be a smooth affine spherical G-variety, both defined over the complex numbers. A well-known theorem of I. Losev's says that 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 the combinatorial theory of spherical varieties and a smoothness criterion of R. Camus to characterize the weight monoids of smooth affine spherical varieties.

Authors with CRIS profile

Bart van Steirteghem Lehrstuhl für Mathematik (Algebra und Geometrie)

Involved external institutions

Università degli studi "La Sapienza" IT Italy (IT)

How to cite

APA:

Pezzini, G., & van Steirteghem, B. (2019). COMBINATORIAL CHARACTERIZATION OF THE WEIGHT MONOIDS OF SMOOTH AFFINE SPHERICAL VARIETIES. Transactions of the American Mathematical Society, 372(4), 2875-2919. https://dx.doi.org/10.1090/tran/7785

MLA:

Pezzini, Guido, and Bart van Steirteghem. "COMBINATORIAL CHARACTERIZATION OF THE WEIGHT MONOIDS OF SMOOTH AFFINE SPHERICAL VARIETIES." Transactions of the American Mathematical Society 372.4 (2019): 2875-2919.

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