On Pl\"ucker Equations Characterizing Grassmann Cones
Abstract
Polynomial solutions to the KP hierarchy are known to be parametrized by a cone over an infinite-dimensional Grassmann variety. Using the notion of Schubert derivation on a Grassmann algebra, we encode the classical Pl\"ucker equations of Grassmannians of r-dimensional subspaces in a formula whose limit for r→∞ coincides with the KP hierarchy phrased in terms of vertex operators.
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