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Elliptic determinant evaluations and the Macdonald identities for affine root systems

Published online by Cambridge University Press:  14 July 2006

Hjalmar Rosengren  and
Michael Schlosser
Hjalmar Rosengren
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Swedenhjalmar@math.chalmers.se
Michael Schlosser
Affiliation:
Fakultät für Mathematik der Universität Wien, Nordbergstraße 15, A-1090 Wien, Austriaschlosse@ap.univie.ac.at
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Abstract

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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.

Keywords

determinantstheta functionselliptic functionsaffine root systemsWeyl denominator formulaMacdonald identities15A15 (primary)17B6733E05 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 4 , July 2006 , pp. 937 - 961
Copyright
Foundation Compositio Mathematica 2006