An application of collapsing levels to the representation theory of affine vertex algebras
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2018
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| _version_ | 1866915042607235072 |
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| author | Adamovic, Drazen Kac, Victor G. Frajria, Pierluigi Moseneder Papi, Paolo Perse, Ozren |
| author_facet | Adamovic, Drazen Kac, Victor G. Frajria, Pierluigi Moseneder Papi, Paolo Perse, Ozren |
| contents | We discover a large class of simple affine vertex algebras $V_{k} (\mathfrak g)$, associated to basic Lie superalgebras $\mathfrak g$ at non-admissible collapsing levels $k$, having exactly one irreducible $\mathfrak g$-locally finite module in the category ${\mathcal O}$. In the case when $\mathfrak g$ is a Lie algebra, we prove a complete reducibility result for $V_k(\mathfrak g)$-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra $V^k (\mathfrak g)$ 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 non-trivial ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_09880 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An application of collapsing levels to the representation theory of affine vertex algebras Adamovic, Drazen Kac, Victor G. Frajria, Pierluigi Moseneder Papi, Paolo Perse, Ozren Representation Theory Mathematical Physics Quantum Algebra 17B69, 17B67, 17B68 We discover a large class of simple affine vertex algebras $V_{k} (\mathfrak g)$, associated to basic Lie superalgebras $\mathfrak g$ at non-admissible collapsing levels $k$, having exactly one irreducible $\mathfrak g$-locally finite module in the category ${\mathcal O}$. In the case when $\mathfrak g$ is a Lie algebra, we prove a complete reducibility result for $V_k(\mathfrak g)$-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra $V^k (\mathfrak g)$ 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 non-trivial ideal. |
| title | An application of collapsing levels to the representation theory of affine vertex algebras |
| topic | Representation Theory Mathematical Physics Quantum Algebra 17B69, 17B67, 17B68 |
| url | https://arxiv.org/abs/1801.09880 |