Journal of Algebraic Combinatorics

, Volume 8, Issue 2, pp 115–126

On Elliptic Product Formulas for Jackson Integrals Associated with Reduced Root Systems

Authors

  • Kazuhiko Aomoto
    • Graduate School of MathematicsNagoya University
Article

DOI: 10.1023/A:1008629309210

Cite this article as:
Aomoto, K. Journal of Algebraic Combinatorics (1998) 8: 115. doi:10.1023/A:1008629309210

Abstract

In this note, we state certain product formulae for Jackson integrals associated with any root systems, involved in elliptic theta functions which appear as connection coefficients. The fomulae arise naturally in case of arbitrary root systems by extending the connection problem which has been investigated in [1, 4] in case ofA type root system. This is also connected with the Macdonald-Morris constant term identity investigated by I. Cherednik [6], and K. Kadell [15] on the one hand, and of the Askey-Habsieger-Kadell's q-Selberg integral formula and its extensions [4, 8, 12, 14, 15] on the other. This is also related with some of the results due to R.A. Gustafson [10, 11], although our integrands are different from his.

elliptic theta functionJackson integralreduced root systemproduct formulaq-difference
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© Kluwer Academic Publishers 1998