2005/08/22 by John S. Caughman, Mark S. MacLean, Caughman, John S. +4 · 1 citation
Computer Science · Mathematics · #05E30 #Advanced Algebra and Geometry #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.CO #math.RT #msc:05E30
paper · pdf · doi:10.48550/arxiv.math/0508401
22 pages
arxiv created 2005/08/22 · openalex publication_date 2005/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Y denote a D-class symmetric association scheme with D ≥ 3, and suppose Y is almost-bipartite P- and Q-polynomial. Let x denote a vertex of Y and let T=T(x) denote the corresponding Terwilliger algebra. We prove that any irreducible T-module W is both thin and dual thin in the sense of Terwilliger. We produce two bases for W and describe the action of T on these bases. We prove that the isomorphism class of W as a T-module is determined by two parameters, the dual endpoint and diameter of W. We find a recurrence which gives the multiplicities with which the irreducible T-modules occur in the standard module. We compute this multiplicity for those irreducible T-modules which have diameter at least D-3.