Generalized n-gons and Chebychev polynomials

Abstract

Two sequences of orthogonal polynomials are given whose weight functions consist of an absolutely continuous part and two point masses. Combinatorial proofs of the orthogonality relations are given. The polynomials include natural q -analogs of the Chebychev polynomials. The technique uses association schemes of generalized n -gons to find approximating discrete orthogonality relations. The Feit-Higman Theorem is a corollary of these orthogonality relations for the polynomials.