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arXiv · 2312.12229

Fay Identities of Pfaffian Type for Hyperelliptic Curves

Gaëtan Borot·Thomas Buc-d'Alché
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Abstract

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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Gaëtan Borot, Thomas Buc-d'Alché. 2023-12-19. Fay Identities of Pfaffian Type for Hyperelliptic Curves. https://doi.org/10.3842/sigma.2024.054

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