Let G be a semisimple complex algebraic group, and H ⊆ G a wonderful subgroup. We prove several results relating the subgroup H to the properties of a combinatorial invariant S of G/H, called its spherical system. It is also possible to consider a spherical system S as a datum defined by purely combinatorial axioms, and under certain circumstances our results prove the existence of a wonderful subgroup H associated with S. As a byproduct, we reduce for any group G the proof of the classification of wonderful G-varieties, known as the Luna conjecture, to its verification on a small family of cases, called primitive. © 2014 Elsevier Inc.

Wonderful subgroups of reductive groups and spherical systems / Bravi, Paolo; Pezzini, Guido. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 409(2014), pp. 101-147.

Wonderful subgroups of reductive groups and spherical systems

BRAVI, Paolo;PEZZINI, Guido
2014

Abstract

Let G be a semisimple complex algebraic group, and H ⊆ G a wonderful subgroup. We prove several results relating the subgroup H to the properties of a combinatorial invariant S of G/H, called its spherical system. It is also possible to consider a spherical system S as a datum defined by purely combinatorial axioms, and under certain circumstances our results prove the existence of a wonderful subgroup H associated with S. As a byproduct, we reduce for any group G the proof of the classification of wonderful G-varieties, known as the Luna conjecture, to its verification on a small family of cases, called primitive. © 2014 Elsevier Inc.
File allegati a questo prodotto
File Dimensione Formato  
Bravi_Wonderful-subgroups_2014.pdf

solo utenti autorizzati

Note: Articolo
Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 681.08 kB
Formato Adobe PDF
681.08 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Bravi_preprint_Wonderful-subgroups_2014.pdf

accesso aperto

Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 597.69 kB
Formato Adobe PDF
597.69 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/11573/560196
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 17
social impact