Invariance of 𝑅-groups between 𝑝-adic inner forms of quasi-split classical groups

Abstract

We study the reducibility of parabolically induced representations of non-split inner forms of quasi-split classical groups. The isomorphism of Arthur R R –groups, endoscopic R R –groups and Knapp-Stein R R –groups is established, as well as showing these R R –groups are isomorphic to the corresponding ones for the quasi-split form. This shows R R –groups are an invariant of the L L –packets. The results are applied to classify the elliptic spectrum.