Fay Identities of Pfaffian Type for Hyperelliptic Curves
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Published:2024-06-23
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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Short-container-title:SIGMA
Author:
,Borot Gaëtan, , ,Buc-d'Alché Thomas,
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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)