An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras
Name
1801.09880.pdf
Description
Accepted version
Size
389.54 KB
Format
Adobe PDF
Checksum (MD5)
98b3fce858c1414b9f55b81ecf019dc1
Author(s)
Adamović, Dražen
Kac, Victor G
Möseneder Frajria, Pierluigi
Papi, Paolo
Perše, Ozren
Date Issued
2018
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Version
Author's final manuscript
Abstract
© 2018 The Author(s). Published by Oxford University Press. All rights reserved. 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/IMRN/RNY237
