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Structure of thin irreducible modules of a Q-polynomial distance-regular graph

โœ Scribed by Diana R. Cerzo

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
562 KB
Volume
433
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

i=0 the polynomials involved are orthogonal and we display the orthogonality relations. We also show that each of the sequences satisfy a three-term recurrence and a relation known as the Askey-Wilson duality. We then turn our attention to two more bases for W. We find the matrix representations of A and A * with respect to these bases. From the entries of these matrices we obtain two sequences of scalars known as the first split sequence and second split sequence of W. We associate with W a sequence of scalars called the parameter array. This sequence consists of the eigenvalues of the restriction of A to W , the eigenvalues of the restriction of A * to W, the first split sequence of W and the second split sequence of W . We express all the scalars and polynomials associated with W in terms of its parameter array. We show that the parameter array of W is determined by r, t, d and one more free parameter. From this we conclude that the isomorphism class of W is determined by these four parameters. Finally, we apply our results to the case in which ฮ“ has q-Racah type or classical parameters.

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