R-groups and parameters

Abstract

Let G be a p-adic group, SO2nC1, Sp 2n , O2n or Un. Let be an irreducible discrete series representation of a Levi subgroup of G. We prove the conjecture that the Knapp‐Stein R-group of and the Arthur R-group of are isomorphic. Several instances of the conjecture were established earlier: for archimedean groups by Shelstad; for principal series representations by Keys; for G D SO2nC1 by Ban and Zhang; and for G D SOn or Sp2n in the case when is supercuspidal, under an assumption on the parameter, by Goldberg.