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.

Combinatorial characterization of the weight monoids of smooth affine spherical varieties / Pezzini, Guido; Van Steirteghem, Bart. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - (2019).

Combinatorial characterization of the weight monoids of smooth affine spherical varieties

PEZZINI, Guido;VAN STEIRTEGHEM, BART
2019

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.
File allegati a questo prodotto
File Dimensione Formato  
Pezzini_postprint_Combinatorial-characterization_2019.pdf

accesso aperto

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 566.69 kB
Formato Adobe PDF
566.69 kB Adobe PDF Visualizza/Apri PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/1274774
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 2
social impact