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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.04571 |
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| _version_ | 1866909579491672064 |
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| author | Ohkawa, Ryo Shiraishi, Jun'ichi |
| author_facet | Ohkawa, Ryo Shiraishi, Jun'ichi |
| contents | We study $K$-theoretic integrals over famed quiver moduli via wall-crossing phenomena. We study the chainsaw quiver varieties, and consider generating functions defined by two types of $K$-theoretic classes. In particular, we focus on integrals over the handsaw quiver varieties of type $A_{1}$, and get functional equations for each of them. We also give explicit formula for these partition functions. In particular, we obtain geometric interpretation of transformation formulas for multiple basic hypergeometric series including the Kajihara transformation formula, and the one studied by Langer-Schlosser-Warnaar and Hallnäs-Langman-Noumi-Rosengren. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $K$-theoretic wall-crossing formulas and multiple basic hypergeometric series Ohkawa, Ryo Shiraishi, Jun'ichi Algebraic Geometry We study $K$-theoretic integrals over famed quiver moduli via wall-crossing phenomena. We study the chainsaw quiver varieties, and consider generating functions defined by two types of $K$-theoretic classes. In particular, we focus on integrals over the handsaw quiver varieties of type $A_{1}$, and get functional equations for each of them. We also give explicit formula for these partition functions. In particular, we obtain geometric interpretation of transformation formulas for multiple basic hypergeometric series including the Kajihara transformation formula, and the one studied by Langer-Schlosser-Warnaar and Hallnäs-Langman-Noumi-Rosengren. |
| title | $K$-theoretic wall-crossing formulas and multiple basic hypergeometric series |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2402.04571 |