On Plücker 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 Plücker equations of Grassmannians of r-dimensional subspaces in a formula whose limit for $r\to \infty$ coincides with the KP hierarchy phrased in terms of vertex operators.

20 Pages

References in corpus (2)

• A categorification of the boson-fermion correspondence via representation theory of $sl(\infty)
• Quantum cohomology and the Satake isomorphism

Cited by in corpus (3)

• The Cohomology of the Grassmannian is a $g{l}_n$-module
• Multivariate Hasse-Schmidt Derivation on Exterior Algebras
• Schur Polynomials and Plücker degree of Schubert Varieties