Abstract
We investigate geometric properties of the (Sato-Segal-Wilson) Grassmannian and its submanifolds, with special attention to the orbits of the KP flows. We use a coherentstates model, by which Spera and Wurzbacher gave equations for the image of a product of Grassmannians using the Powers-Stormer purification procedure. We extend to this product Sato’s idea of turning equations that define the projective embedding of a homogeneous space into a hierarchy of partial differential equations. We recover the BKP equations from the classical Segre embedding by specializing the equations to finite-dimensional submanifolds.
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