‎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 w...

Introduction 1 1. Notation and conventions 8 2. Shimura varieties for unitary groups 13 3. Modular forms on unitary groups 23 4. Hida theory for unitary groups 36 5. Ordinary p-adic Eisenstein series on U(2, 1) 52 6. Constant terms of the p-adic Eisenstein series 68 7. Eisenstein ideal and p-adic L-functions 76 8. Application to the main conjecture for CM fields 93 Acknowledgments 107 Reference...

The orbit method conjectures a close relationship between the set of irreducible unitary representations of a Lie group G, and admissible coadjoint orbits in the dual of the Lie algebra. We define admissibility for nilpotent coadjoint orbits of p-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples. We find that for unitary, symplectic, orthogonal, general...