Symmetry Classification for Jackson Integrals Associated with Irreducible Reduced Root Systems |
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Authors: | Masahiko Ito |
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Institution: | (1) Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan |
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Abstract: | 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 F
4 root system is included in it. |
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Keywords: | Jackson integrals Aomoto's sums Gustafson's sums van Diejen's BC
n
-type sum |
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