Polarization Tensors for the fuzzy Grassmannians $Gr_{2;n}^F$ and Grassmannian harmonics on $Gr_{2;n}$

TL;DR

This paper constructs explicit eigenfunctions and spectra of the Laplacian on fuzzy Grassmannian spaces, providing new harmonic expressions in terms of Plücker coordinates that resemble free particle wave functions.

Contribution

It introduces explicit eigenfunctions and spectra for the Laplacian on fuzzy Grassmannians and offers a novel harmonic representation using Plücker coordinates.

Findings

Eigenfunctions explicitly constructed for fuzzy Grassmannians

Spectrum is a truncation of the continuum case

Grassmannian harmonics expressed via Plücker coordinates

Abstract

We explicitly construct the eigenfunctions of the Laplacian for the fuzzy Grassmannian spaces $Gr_{2;n}^F$. We calculate the spectrum and find it be a truncation of the continuum case. As a byproduct of our approach we find a novel expression for the Grassmannian harmonics in terms of Plucker coordinates which can be interpreted as free Schrodinger particle wave functions on $Gr_{2;n}$.