Elliptic Selberg integrals

We introduce new Selberg-type multidimensional integrals built of Ruijsenaars' elliptic gamma functions. We show that the vanishing of our integrals for a specific parameter hypersurface implies closed evaluation formulas valid for the full parameter space. The resulting integration formulas contain the Macdonald-Morris constant term identities for nonreduced root systems as special limiting cases.