Characters of (relatively) integrable modules over affine Lie superalgebras
In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules L over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras g. The problem consists of two parts. First, it is the reduction of the problem to the [ba...
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| Format: | Article |
| Language: | English |
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Springer Japan
2016
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| Online Access: | http://hdl.handle.net/1721.1/104442 https://orcid.org/0000-0002-2860-7811 |
| _version_ | 1811072381371809792 |
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| author | Gorelik, Maria Kac, Victor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Gorelik, Maria Kac, Victor |
| author_sort | Gorelik, Maria |
| collection | MIT |
| description | In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules L over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras g. The problem consists of two parts. First, it is the reduction of the problem to the [bar over g]-module F(L), where [bar over g] is the associated to L integral Lie superalgebra and F(L) is an integrable irreducible highest weight [bar over g]-module. Second, it is the computation of characters of integrable highest weight modules. There is a general conjecture concerning the first part, which we check in many cases. As for the second part, we prove in many cases the KW-character formula, provided that the KW-condition holds, including almost all finite-dimensional g-modules when g is basic, and all maximally atypical non-critical integrable g-modules when g is affine with non-zero dual Coxeter number. |
| first_indexed | 2024-09-23T09:05:11Z |
| format | Article |
| id | mit-1721.1/104442 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:05:11Z |
| publishDate | 2016 |
| publisher | Springer Japan |
| record_format | dspace |
| spelling | mit-1721.1/1044422022-09-30T13:20:42Z Characters of (relatively) integrable modules over affine Lie superalgebras Gorelik, Maria Kac, Victor Massachusetts Institute of Technology. Department of Mathematics Kac, Victor In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules L over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras g. The problem consists of two parts. First, it is the reduction of the problem to the [bar over g]-module F(L), where [bar over g] is the associated to L integral Lie superalgebra and F(L) is an integrable irreducible highest weight [bar over g]-module. Second, it is the computation of characters of integrable highest weight modules. There is a general conjecture concerning the first part, which we check in many cases. As for the second part, we prove in many cases the KW-character formula, provided that the KW-condition holds, including almost all finite-dimensional g-modules when g is basic, and all maximally atypical non-critical integrable g-modules when g is affine with non-zero dual Coxeter number. Simons Foundation. Postdoctoral Fellowship 2016-09-29T18:39:47Z 2016-09-29T18:39:47Z 2015-06 2015-03 2016-08-18T15:22:05Z Article http://purl.org/eprint/type/JournalArticle 0289-2316 1861-3624 http://hdl.handle.net/1721.1/104442 Gorelik, Maria, and Victor G. Kac. “Characters of (Relatively) Integrable Modules over Affine Lie Superalgebras.” Japanese Journal of Mathematics 10.2 (2015): 135–235. https://orcid.org/0000-0002-2860-7811 en http://dx.doi.org/10.1007/s11537-015-1464-2 Japanese Journal of Mathematics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ The Mathematical Society of Japan and Springer Japan application/pdf Springer Japan Springer Japan |
| spellingShingle | Gorelik, Maria Kac, Victor Characters of (relatively) integrable modules over affine Lie superalgebras |
| title | Characters of (relatively) integrable modules over affine Lie superalgebras |
| title_full | Characters of (relatively) integrable modules over affine Lie superalgebras |
| title_fullStr | Characters of (relatively) integrable modules over affine Lie superalgebras |
| title_full_unstemmed | Characters of (relatively) integrable modules over affine Lie superalgebras |
| title_short | Characters of (relatively) integrable modules over affine Lie superalgebras |
| title_sort | characters of relatively integrable modules over affine lie superalgebras |
| url | http://hdl.handle.net/1721.1/104442 https://orcid.org/0000-0002-2860-7811 |
| work_keys_str_mv | AT gorelikmaria charactersofrelativelyintegrablemodulesoveraffineliesuperalgebras AT kacvictor charactersofrelativelyintegrablemodulesoveraffineliesuperalgebras |