Elliptic determinant evaluations and the Macdonald identities for affine   root systems
  We obtain several determinant evaluations, related to affine root systems, which provide elliptic extensions of Weyl denominator formulas. Some of these are new, also in the polynomial special case, while others yield new proofs of the Macdonald identities for the seven infinite families of irreducible reduced affine root systems. 
Hjalmar Rosengren and Michael Schlosser