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Symmetry Classification for Jackson Integrals Associated with Irreducible Reduced Root Systems

Published online by Cambridge University Press:  04 December 2007

Masahiko Ito
Masahiko Ito
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan. E-mail: mito@math.nagoya-u.ac.jp
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Abstract

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We state certain product formulae for Jackson integrals associated with irreducible reduced root systems. The Jackson integral is defined here as a sum over any full-rank sublattice of the coweight lattice for the root system. In particular, a Weyl group symmetry classification of the Jackson integrals is done when they have an expression of a product of the Jacobi elliptic theta functions. Most of the product formulae investigated by Aomoto, Macdonald and Gustafson appear in the list of classifications. A new product formula for an F4 root system is included in it.

Keywords

Jackson integralsAomoto's sumsGustafson's sumsvan Diejen's BCn-type sum
Type
Research Article
Information
Compositio Mathematica , Volume 129 , Issue 3 , December 2001 , pp. 325 - 340
Copyright
© 2001 Kluwer Academic Publishers