Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups

Abstract

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This work is applied to transferring known results in the second-named author's earlier work for quasi-split special unitary groups to their non-quasi-split inner forms‎.