Elliptic determinant evaluations and the Macdonald identities for affine root systems

Abstract

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.

26 pages; minor modifications; to appear in Compositio Math

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