We discover a large class of simple affine vertex algebras Vk(g), associated to basic Lie superalgebras g at non-admissible collapsing levels k, having exactly one irreducible g-locally finite module in the category O. In the case when g is a Lie algebra, we prove a complete reducibility result for Vk(g)-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra Vk(g) at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras V−1/2(Cn) and V−4(E7), we surprisingly obtain the realization of non-simple affine vertex algebras of types B and D having exactly one nontrivial ideal.

An application of collapsing levels to the representation theory of affine vertex algebras / Adamovic, Drazen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perse, Ozren. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1687-0247. - 13:(2020), pp. 4103-4143. [10.1093/imrn/rny237]

An application of collapsing levels to the representation theory of affine vertex algebras

Paolo Papi;
2020

Abstract

We discover a large class of simple affine vertex algebras Vk(g), associated to basic Lie superalgebras g at non-admissible collapsing levels k, having exactly one irreducible g-locally finite module in the category O. In the case when g is a Lie algebra, we prove a complete reducibility result for Vk(g)-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra Vk(g) at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras V−1/2(Cn) and V−4(E7), we surprisingly obtain the realization of non-simple affine vertex algebras of types B and D having exactly one nontrivial ideal.
vertex algebras; conformal embedding; affine Lie superalgebra
01 Pubblicazione su rivista::01a Articolo in rivista
An application of collapsing levels to the representation theory of affine vertex algebras / Adamovic, Drazen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perse, Ozren. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1687-0247. - 13:(2020), pp. 4103-4143. [10.1093/imrn/rny237]
File allegati a questo prodotto
File Dimensione Formato  
Adamovic_preprint_An-application_2020.pdf

accesso aperto

Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Creative commons
Dimensione 389.54 kB
Formato Adobe PDF
389.54 kB Adobe PDF Visualizza/Apri PDF
Adamovic_An-application_2020.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 419.88 kB
Formato Adobe PDF
419.88 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: https://hdl.handle.net/11573/1180890
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact