On odd-spin $A_{1}^{(1)}$-string functions, cross-spin identities, and mock theta conjecture-like identities
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911503049818112 |
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| author | Konenkov, Stepan Mortenson, Eric T. |
| author_facet | Konenkov, Stepan Mortenson, Eric T. |
| contents | Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is a long-standing, yet wide-open, problem and recently a connection has been made between positive admissible-level $A_{1}^{(1)}$-string functions and Ramanujan's mock theta functions. In this paper we obtain the polar-finite decomposition for the admissible-level $A_{1}^{(1)}$ character of odd spin, and we also find new mock theta conjecture-like identities for the odd-spin, $2/3$-level and $2/5$-level $A_{1}^{(1)}$-string functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On odd-spin $A_{1}^{(1)}$-string functions, cross-spin identities, and mock theta conjecture-like identities Konenkov, Stepan Mortenson, Eric T. Number Theory Representation Theory Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is a long-standing, yet wide-open, problem and recently a connection has been made between positive admissible-level $A_{1}^{(1)}$-string functions and Ramanujan's mock theta functions. In this paper we obtain the polar-finite decomposition for the admissible-level $A_{1}^{(1)}$ character of odd spin, and we also find new mock theta conjecture-like identities for the odd-spin, $2/3$-level and $2/5$-level $A_{1}^{(1)}$-string functions. |
| title | On odd-spin $A_{1}^{(1)}$-string functions, cross-spin identities, and mock theta conjecture-like identities |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2603.08437 |