Constant term identities, orthogonal polynomials and affine Hecke algebras (Q1129851)

This is an overview of developments that began with constant term identities indexed by root systems. In the late 1980s, the author recognized that these identities could be recast as a special case of norm evaluations for a natural family of orthogonal polynomials that are invariant under the symmetries of the corresponding Weyl group and that have coefficients in the field of rational functions in two indeterminants, \(q\) and \(t\). Symmetric functions, Weyl characters, and classical orthogonal polynomials all arise as special cases. The author describes results for these polynomials, results that culminate in recent extensions to affine Hecke algebras.