K-theoretic wall-crossing formulas and multiple basic hypergeometric series
We study K-theoretic integrals over framed 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 A1, and get func...
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| Veröffentlicht in: | Journal of algebra Jg. 677; S. 516 - 584 |
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| Abstract | We study K-theoretic integrals over framed 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 A1, 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. |
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| AbstractList | We study K-theoretic integrals over framed 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 A1, 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. |
| Author | Ohkawa, R. Shiraishi, J. |
| Author_xml | – sequence: 1 givenname: R. orcidid: 0009-0000-7508-2862 surname: Ohkawa fullname: Ohkawa, R. email: ohkawa.ryo@gmail.com organization: Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan – sequence: 2 givenname: J. surname: Shiraishi fullname: Shiraishi, J. organization: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan |
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| Cites_doi | 10.4310/PAMQ.2017.v13.n3.a6 10.1016/S0019-3577(03)90054-1 10.1093/qmath/45.4.515 10.1215/21562261-1214366 10.4310/ATMP.2003.v7.n5.a4 10.17323/1609-4514-2020-20-3-531-573 10.1016/S0040-9383(98)00042-1 10.1215/S0012-7094-92-06817-7 10.1090/jag/738 10.1023/A:1017558904030 10.1007/s00220-022-04360-7 10.17323/1609-4514-2012-12-3-633-666 10.1007/BF01388892 10.1007/s11005-018-1071-2 10.1215/00127094-1593380 10.1016/j.geomphys.2023.104904 10.1007/s00222-005-0444-1 10.1215/S0012-7094-00-10239-6 10.1007/s00029-021-00745-z 10.1007/s002220050136 10.1016/j.aim.2003.08.012 10.1016/j.jalgebra.2008.01.025 10.1007/s002220050293 |
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| Keywords | Affine Laumon function Handsaw quiver variety Framed quiver moduli Multiple basic hypergeometric series Kajihara transformation Wall-crossing formula Chainsaw quiver variety Non-stationary Ruijsenaars function |
| Language | English |
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| Snippet | We study K-theoretic integrals over framed quiver moduli via wall-crossing phenomena. We study the chainsaw quiver varieties, and consider generating functions... |
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| SubjectTerms | Affine Laumon function Chainsaw quiver variety Framed quiver moduli Handsaw quiver variety Kajihara transformation Multiple basic hypergeometric series Non-stationary Ruijsenaars function Wall-crossing formula |
| Title | K-theoretic wall-crossing formulas and multiple basic hypergeometric series |
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