The sl3 Selberg integral

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 sl3 generalisation of the famous Selberg integral. Closely related results obtained in this paper are an sl3-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.