Associative algebras, Combinatorial analysis, Irreducible polynomials
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.
© 2005 Elsevier B.V. All rights reserved
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Published as: John S. Caughman, Mark S. MacLean, Paul M. Terwilliger (2005). The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme, Discrete Mathematics, Volume 292, Issues 1–3, Pages 17-44.
NOTICE: this is the author’s version of a work that was accepted for publication in Discrete Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Mathematics, VOL 292, ISSUE 1-3, 2005 DOI: 10.1016/j.disc.2004.12.001
*At the time of publication John S. Caughman was affiliated with the University of North Carolina at Asheville.