Elliptic determinant evaluations and the Macdonald identities for affine root systems

Details Elliptic determinant evaluations and the Macdonald identities for affine root systems Elliptic determinant evaluations and the Macdonald identities for affine root systems

2005-05-11

arxiv.org/abs/math/0505213v2

Compositio Math. 142 (2006), 937-961

Mathematics

Classical Analysis and ODEs

26 pages; minor modifications; to appear in Compositio Math

Scientific paper

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.

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