On elliptic product formulas for jackson integrals associated with reduced root systems

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 of A 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.