Tight Frames for Eigenspaces of the Laplacian on Dual Polar Graphs

TL;DR

This paper constructs tight frames for each eigenspace of the Laplacian on dual polar graphs, providing explicit constants and a formula for Norton algebra multiplication related to the second largest eigenvalue.

Contribution

It introduces explicit tight frames for Laplacian eigenspaces on dual polar graphs and derives formulas for Norton algebra operations, advancing spectral graph theory.

Findings

Explicit tight frames for all Laplacian eigenspaces

Computed constants for each tight frame

Derived a formula for Norton algebra multiplication

Abstract

We consider $\Gamma=(X,E)$ a dual polar graph and we give a tight frame on each eigenspace of the Laplacian operator associated to $\Gamma$. We compute the constants associated to each tight frame and as an application we give a formula for the product in the Norton algebra attached to the eigenspace corresponding to the second largest eigenvalue of the Laplacian.