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The Schur function expansion of Sato-Segal-Wilson KP tau-functions isreviewed. The case of tau-functions related to algebraic curves of arbitrarygenus is studied in detail. Explicit expressions for the Pl\"ucker coordinatecoefficients appearing in the expansion are obtained in terms of directionalderivatives of the Riemann theta function or Klein sigma function along the KPflow directions. Using the fundamental bi-differential, it is shown how thecoefficients can be expressed as polynomials in terms of Klein's higher genusgeneralizations of Weierstrass' zeta and P functions. The cases of genus twohyperelliptic and genus three trigonal curves are detailed as illustrations ofthe approach developed here.

Schur function expansions of KP tau functions associated to algebraic curves