Fay Identities of Pfaffian Type for Hyperelliptic Curves - Borot, Gaëtan; Buc-d'Alché, Thomas (Symmetry, Integrability and Geometry: Methods and Applications, 2024)
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.