  Using an extension of the well-known evaluation symmetry, a new Cauchy-type
identity for Macdonald polynomials is proved. After taking the classical limit
this yields a new sl_3 generalisation of the famous Selberg integral. Closely
related results obtained in this paper are an sl_3-analogue of the
Askey-Habsieger-Kadell q-Selberg integral and an extension of the q-Selberg
integral to a transformation between q-integrals of different dimensions.
