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
MathSciNet review:
3988597
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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.
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Additional Information
Guido Pezzini
Affiliation:
Dipartimento di Matematica “Guido Castelnuovo”, “Sapienza” Università di Roma, Rome, Italy
MR Author ID:
772887
Email:
pezzini@mat.uniroma1.it
Bart Van Steirteghem
Affiliation:
Department Mathematik, Emmy–Noether–Zentrum, FAU Erlangen-Nürnberg, Erlangen, Germany; and Department of Mathematics, Medgar Evers College—City University of New York, Brooklyn, New York
MR Author ID:
646175
Email:
bartvs@mec.cuny.edu
Received by editor(s):
April 4, 2017
Received by editor(s) in revised form:
August 7, 2018, and October 28, 2018
Published electronically:
February 25, 2019
Additional Notes:
The first author was partially supported by the DFG Schwerpunktprogramm 1388—Darstellungstheorie.
The second author received support from the City University of New York PSC-CUNY Research Award Program, and from the National Science Foundation through grant DMS 1407394. He also thanks Medgar Evers College for his 2016-17 Fellowship Award.
Article copyright:
© Copyright 2019
American Mathematical Society
