A Conjecture of Warnaar-Zudilin from Deformations of Lie Superalgebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929683038208000 |
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| author | Creutzig, Thomas Garner, Niklas |
| author_facet | Creutzig, Thomas Garner, Niklas |
| contents | We prove a collection of $q$-series identities conjectured by Warnaar and Zudilin and appearing in recent work with H. Kim in the context of superconformal field theory. Our proof utilizes a deformation of the simple affine vertex operator superalgebra $L_k(\mathfrak{osp}_{1|2n})$ into the principal subsuperspace of $L_k(\mathfrak{sl}_{1|2n+1})$ in a manner analogous to earlier work of Feigin-Stoyanovsky. This result fills a gap left by Stoyanovsky, showing that for all positive integers $N$, $k$ the character of the principal subspace of type $A_N$ at level $k$ can be identified with the (super)character of a simple affine vertex operator (super)algebra at the same level. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_11509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Conjecture of Warnaar-Zudilin from Deformations of Lie Superalgebras Creutzig, Thomas Garner, Niklas Quantum Algebra High Energy Physics - Theory Number Theory Representation Theory We prove a collection of $q$-series identities conjectured by Warnaar and Zudilin and appearing in recent work with H. Kim in the context of superconformal field theory. Our proof utilizes a deformation of the simple affine vertex operator superalgebra $L_k(\mathfrak{osp}_{1|2n})$ into the principal subsuperspace of $L_k(\mathfrak{sl}_{1|2n+1})$ in a manner analogous to earlier work of Feigin-Stoyanovsky. This result fills a gap left by Stoyanovsky, showing that for all positive integers $N$, $k$ the character of the principal subspace of type $A_N$ at level $k$ can be identified with the (super)character of a simple affine vertex operator (super)algebra at the same level. |
| title | A Conjecture of Warnaar-Zudilin from Deformations of Lie Superalgebras |
| topic | Quantum Algebra High Energy Physics - Theory Number Theory Representation Theory |
| url | https://arxiv.org/abs/2501.11509 |