Generalized Chebyshev Polynomials Associated with Affine Weyl Groups

Michael E. Hoffman, William Douglas Withers
1988 Transactions of the American Mathematical Society  
We begin with a compact figure that can be folded into smaller replicas of itself, such as the interval or equilateral triangle. Such figures are in one-to-one correspondence with affine Weyl groups. For each such figure in n-dimensional Euclidean space, we construct a sequence of polynomials P/c: Rn -► Rn so that the mapping P^ is conjugate to stretching the figure by a factor A; and folding it back onto itself. If re = 1 and the figure is the interval, this construction yields the Chebyshev
more » ... lds the Chebyshev polynomials (up to conjugation). The polynomials Pk are orthogonal with respect to a suitable measure and can be extended in a natural way to a complete set of orthogonal polynomials.
doi:10.2307/2000951 fatcat:iuwqmk2g4bcqxdk5kmdrmvcmfi