On the classification of non-equal rank affine conformal embeddings and applications
© 2018, Springer International Publishing AG, part of Springer Nature. We complete the classification of conformal embeddings of a maximally reductive subalgebra k into a simple Lie algebra g at non-integrable non-critical levels k by dealing with the case when k has rank less than that of g. We des...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Science and Business Media LLC
2021
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| Online Access: | https://hdl.handle.net/1721.1/134938 |
| _version_ | 1826217265707614208 |
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| author | Adamović, Dražen Kac, Victor G Frajria, Pierluigi Möseneder Papi, Paolo Perše, Ozren |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Adamović, Dražen Kac, Victor G Frajria, Pierluigi Möseneder Papi, Paolo Perše, Ozren |
| author_sort | Adamović, Dražen |
| collection | MIT |
| description | © 2018, Springer International Publishing AG, part of Springer Nature. We complete the classification of conformal embeddings of a maximally reductive subalgebra k into a simple Lie algebra g at non-integrable non-critical levels k by dealing with the case when k has rank less than that of g. We describe some remarkable instances of decomposition of the vertex algebra Vk(g) as a module for the vertex subalgebra generated by k. We discuss decompositions of conformal embeddings and constructions of new affine Howe dual pairs at negative levels. In particular, we study an example of conformal embeddings A1× A1↪ C3 at level k= - 1 / 2 , and obtain explicit branching rules by applying certain q-series identity. In the analysis of conformal embedding A1× D4↪ C8 at level k= - 1 / 2 we detect subsingular vectors which do not appear in the branching rules of the classical Howe dual pairs. |
| first_indexed | 2024-09-23T17:00:38Z |
| format | Article |
| id | mit-1721.1/134938 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:00:38Z |
| publishDate | 2021 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1349382023-01-11T18:53:14Z On the classification of non-equal rank affine conformal embeddings and applications Adamović, Dražen Kac, Victor G Frajria, Pierluigi Möseneder Papi, Paolo Perše, Ozren Massachusetts Institute of Technology. Department of Mathematics © 2018, Springer International Publishing AG, part of Springer Nature. We complete the classification of conformal embeddings of a maximally reductive subalgebra k into a simple Lie algebra g at non-integrable non-critical levels k by dealing with the case when k has rank less than that of g. We describe some remarkable instances of decomposition of the vertex algebra Vk(g) as a module for the vertex subalgebra generated by k. We discuss decompositions of conformal embeddings and constructions of new affine Howe dual pairs at negative levels. In particular, we study an example of conformal embeddings A1× A1↪ C3 at level k= - 1 / 2 , and obtain explicit branching rules by applying certain q-series identity. In the analysis of conformal embedding A1× D4↪ C8 at level k= - 1 / 2 we detect subsingular vectors which do not appear in the branching rules of the classical Howe dual pairs. 2021-10-27T20:09:57Z 2021-10-27T20:09:57Z 2018 2019-11-14T16:36:24Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134938 en 10.1007/S00029-017-0386-7 Selecta Mathematica, New Series Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer Science and Business Media LLC arXiv |
| spellingShingle | Adamović, Dražen Kac, Victor G Frajria, Pierluigi Möseneder Papi, Paolo Perše, Ozren On the classification of non-equal rank affine conformal embeddings and applications |
| title | On the classification of non-equal rank affine conformal embeddings and applications |
| title_full | On the classification of non-equal rank affine conformal embeddings and applications |
| title_fullStr | On the classification of non-equal rank affine conformal embeddings and applications |
| title_full_unstemmed | On the classification of non-equal rank affine conformal embeddings and applications |
| title_short | On the classification of non-equal rank affine conformal embeddings and applications |
| title_sort | on the classification of non equal rank affine conformal embeddings and applications |
| url | https://hdl.handle.net/1721.1/134938 |
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