The Structure of Nonthin Irreducible T-modules of Endpoint 1: Ladder Bases and Classical Parameters
S. Hobart
and T. Ito
DOI: 10.1023/A:1008619211978
Abstract
Building on the work of Terwilliger, we find the structure of nonthin irreducible T-modules of endpoint 1 for P- and Q-polynomial association schemes with classical parameters. The isomorphism class of such a given module is determined by the intersection numbers of the scheme and one additional parameter which must be an eigenvalue for the first subconstituent graph. We show that these modules always have what we call a ladder basis, and find the structure explicitly for the bilinear, Hermitean, and alternating forms schemes.
Pages: 53–75
Keywords: association scheme; Terwilliger algebra
Full Text: PDF
References
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2. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, 1989.
3. K. Tanabe, “The irreducible modules of the Terwilliger algebras of Doob schemes,” J. Alg. Combin. 6 (1997), 173-195.
4. P. Terwilliger, “The subconstituent algebra of an association scheme,” I J. Alg. Combin. 1 (1992), 363-388; II J. Alg. Combin. 2 (1993), 73-103; III J. Alg. Combin. 2 (1993), 177-210.
5. P. Terwilliger, The Subconstituent Algebra of a Graph, the Thin Condition, and the Q-Polynomial Property. Unpublished lecture notes, 1992.
6. P. Terwilliger, “Kite-free distance regular graphs,” Europ. J. Combin. 16 (1995), 405-414.
7. P. Terwilliger, Personal communication.