Fay Identities of Pfaffian Type for Hyperelliptic Curves
We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212253 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Fay Identities of Pfaffian Type for Hyperelliptic Curves. Gaëtan Borot and Thomas Buc-d'Alché. SIGMA 20 (2024), 054, 38 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of orthogonal or quaternionic self-dual random matrices. We show that they amount to identities for the theta function with the period matrix of a hyperelliptic curve, and in this form, we reprove them by direct geometric methods.
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| ISSN: | 1815-0659 |