Transfer of R-groups between p-adic inner forms of SL_n

We study the Knapp-Stein $R$–groups for inner forms of the split group $S{L}_n(F),$ with $F$ a $p$–adic field of characteristic zero. Thus, we consider the groups $S{L}_m(D),$ with $D$ a central division algebra over $F$ of dimension $d^2,$ and $m=n\mathrm{/}d\mathrm{.}$ We use the generalized Jacquet-Langlands correspondence and results of the first named author to describe the zeros of Plancherel measures. Combined with a study of the behavior of the stabilizer of representations by elements of the Weyl group we are able to determine the Knapp-Stein $R$–groups in terms of those for $S{L}_n(F)\mathrm{.}$ We show the $R$–group for the inner form embeds as a subgroup of the $R$–group for the split form, and we characterize the quotient. We are further able to show the Knapp-Stein $R$–group is isomorphic to the Arthur, or Endoscopic $R$–group as predicted by Arthur. Finally, we give some results on multiplicities and actions of Weyl groups on $L$–packets.