Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9513546 | Discrete Mathematics | 2005 | 28 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
John S. Caughman, Mark S. MacLean, Paul M. Terwilliger,