A Dyson Constant Term Orthogonality Relation

We give a constant term orthogonality relation and a conjectured q-analogue which are related to the Dyson constant term identity. This is the fact that the constant term in ∏1⩽i<j⩽n (1−ti/tj)ai (1−tj/ti)aj is the multinomial coefficient (a1+…+an)!/a1!…an!. These and other results suggest that there should exist Dyson polynomials which generalize the Macdonald polynomials.