Let G be a p-adic group,
SO2n+1, Sp2n, O2n or Un. Let π be an irreducible discrete series representation of a
Levi subgroup of G. We prove the conjecture that the Knapp–Stein R-group of π and
the Arthur R-group of π are isomorphic. Several instances of the conjecture were
established earlier: for archimedean groups by Shelstad; for principal series
representations by Keys; for G =SO2n+1 by Ban and Zhang; and for G =SOn or
Sp2n in the case when π is supercuspidal, under an assumption on the parameter, by
Goldberg.
Keywords
R-groups, reducibility of induced representations,
classical groups