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Some algebra related to $$P$$- and $$Q$$-polynomial association schemes. (English) Zbl 0995.05148
Barg, Alexander (ed.) et al., Codes and association schemes. DIMACS workshop, DIMACS Center, Princeton, NJ, USA, November 9-12, 1999. Providence, RI: AMS, American Mathematical Society. DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 56, 167-192 (2001).
Inspired by the theory of $$P$$- and $$Q$$-polynomial association schemes, the authors consider “tridiagonal pairs”, i.e., pairs of linear transformations, which are diagonalizable and satisfy certain conditions on the eigenspaces. Various results concerning the dimensions of these eigenspaces are proved. These can be viewed as steps towards a classification of all tridiagonal pairs.
For the entire collection see [Zbl 0960.00079].

##### MSC:
 05E30 Association schemes, strongly regular graphs 15A21 Canonical forms, reductions, classification 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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