Higher level BGG reciprocity for current algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914051469082624 |
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| author | Kato, Syu |
| author_facet | Kato, Syu |
| contents | We exhibit a higher-level analogue of the Bernstein-Gelfand-Gelfand (BGG) reciprocity for twisted current algebras for each positive integer, which recovers the original one (established by Bennett, Berenstein, Chari, Ion, Khoroshkin, Loktev, and Manning) as its level-one case. This work brings theta functions and modular forms into the theory of symmetric polynomials. Furthermore, we establish branching properties for both versions of Demazure modules and provide a new interpretation of level-restricted generalized Kostka polynomials in terms of symmetric polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_07447 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Higher level BGG reciprocity for current algebras Kato, Syu Representation Theory Quantum Algebra We exhibit a higher-level analogue of the Bernstein-Gelfand-Gelfand (BGG) reciprocity for twisted current algebras for each positive integer, which recovers the original one (established by Bennett, Berenstein, Chari, Ion, Khoroshkin, Loktev, and Manning) as its level-one case. This work brings theta functions and modular forms into the theory of symmetric polynomials. Furthermore, we establish branching properties for both versions of Demazure modules and provide a new interpretation of level-restricted generalized Kostka polynomials in terms of symmetric polynomials. |
| title | Higher level BGG reciprocity for current algebras |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2207.07447 |