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

Document Type: Special Issue of BIMS in Honor of Professor Freydoon Shahidi

Authors

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.

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### History

• Receive Date: 13 May 2017
• Revise Date: 01 October 2017
• Accept Date: 19 May 2017