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 $r\rightarrow\infty$ coincides with the KP hierarchy phrased in terms of vertex operators.Comment: 20 Page