Classical W-symmetry and Grassmannian Manifold

TL;DR

This paper explores the parametrization of classical W-symmetry using Grassmannian manifolds linked to non-relativistic fermions, introducing bosonization rules and deriving W-algebra generators from tau-functions.

Contribution

It provides a new bosonization framework and connects W-symmetry to Grassmannian geometry, offering a novel approach to W-geometry analysis.

Findings

Grassmannian manifold parametrizes classical W-symmetry

Bosonization rule defines higher coordinates for W-geometry

W-algebra generators derived from tau-functions using vertex operators

Abstract

Classical W-symmetry is globally parametrized by the Grassmannian Manifold which is associated with the non-relativistic fermions. We give the bosonization rule which defines the natural higher coordinates system to describe the W-geometry. Generators of the W-algebra can be obtained from a single tau-function by using vertex operators.