Dual R-groups of the inner forms of SL(N)

Abstract

We study the Knapp-Stein R-groups of the inner forms of SL(N) over a non-archimedean local field of characteristic zero, by using restriction from the inner forms of GL(N). As conjectured by Arthur, these R-groups are then shown to be naturally isomorphic to their dual avatars defined in terms of L-parameters. The 2-cocycles attached to R-groups can be described as well. The proofs are based on the results of K. Hiraga and H. Saito. We also construct examples to illustrate some new phenomena which do not occur in the case of SL(N) or classical groups.

47 pages

References in corpus (3)

• Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition
• R-groups and parameters
• Reducibility for $S{U}_n$ and generic elliptic representations

Cited by in corpus (9)

• Limit multiplicities for principal congruence subgroups of GL(n) and SL(n)
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• On the analytic properties of intertwining operators I: global normalizing factors
• Local Langlands Conjecture for $p$-adic $GSpi{n}_4,$ $GSpi{n}_6,$ and their inner forms
• Hecke algebras for inner forms of p-adic special linear groups
• Transfer of R-groups between p-adic inner forms of SL_n
• $R$--groups, elliptic representations, and parameters for $GSpin$ groups
• Weakly unramified representations, finite morphisms, and Knapp-Stein $R$-groups
• Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups