 extended the conjecture to arbitrary finite or affine root systems, with Dyson's original conjecture corresponding to 
the case of the "A""n"−1 root system and Andrews's conjecture corresponding to the affine "A""n"−1 root system.Macdonald reformulated these conjectures as conjectures about the norms of Macdonald polynomials.Macdonald's conjectures were proved by using doubly affine Hecke algebras.