R-groups and parameters

Abstract

For classical groups we show the isomorphism of the Knapp-Stein $R$-group, which describes the structure of parabolically induced representations, and the Arthur $R$-group of the parameter associated to the inducing representation by the local Langlands conjecture. We do this in the case of inducing from discrete series representations. In the case of unitary groups we show this isomorphism under a mild assumption on the parameter, which we show holds in at least half the cases.