期刊
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
卷 2020, 期 13, 页码 4103-4143出版社
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rny237
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类别
资金
- Croatian Science Foundation [2634]
- QuantiXLie Center of Excellence
- Croatian Government
- European Union through the European Regional Development Fund-the Competitiveness and Cohesion Operational Programme [KK.01.1.1.01]
We discover a large class of simple affine vertex algebras V-k(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 V-k(g)-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra V-k(g) at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras V-1/2(C-n) and V-4(E-7), we surprisingly obtain the realization of non-simple affine vertex algebras of types B and D having exactly one nontrivial ideal.
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