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.
2020
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1180890
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