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Symmetry Classification for Jackson Integrals Associated with the Root System BCn

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: [email protected]
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Abstract

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The Jackson integrals associated with the non-reduced root system are defined as multiple sums which are generalization of the Bailey's very-well-poised 6ψ6 sum. They are classified by the number of their parameters when they can be expressed as a product of the Jacobi elliptic theta functions. The sums which appear in the classification list coincide with those investigated individually by Gustafson and van Diejen.

Keywords

Bailey's very-well-poised 6ψ6 sumGustafson's Cn-type sumJackson integralsnon-reduced root systemvan Diejen's BCn-type sum.
Type
Research Article
Information
Compositio Mathematica , Volume 136 , Issue 2 , April 2003 , pp. 209 - 216
Copyright
© 2003 Kluwer Academic Publishers