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

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 $Gr_{2;n}$.