Tight Frames for Eigenspaces of the Laplacian on Dual Polar Graphs

2009/05/30 by Fernando Levstein, F. Levstein, C. D. Maldonado +6
Mathematics · #05E30 #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.CO #msc:05E30

paper · pdf · doi:10.48550/arxiv.0906.0116

18 pages, no figures

arxiv created 2009/05/30 · openalex publication_date 2009/05/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Γ=(X,E) a dual polar graph and we give a tight frame on each eigenspace of the Laplacian operator associated to Γ. 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.

Related

• Lattices and Norton algebras of Johnson, Grassmann and Hamming graphs
• Tightness of the weight-distribution bound for strongly regular polar graphs
• The Laplacian Eigenvalues and Invariants of Graphs
• Eigenmodes of a Laplacian on Some Laakso Spaces
• Largest Eigenvalue of the Laplacian Matrix