Vol. 267, No. 1, 2014

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Dual $R$-groups of the inner forms of $\mathrm{SL}(N)$

Kuok Fai Chao and Wen-Wei Li

Vol. 267 (2014), No. 1, 35–90

We study the Knapp–Stein R-groups of the inner forms of SL(N) over a nonarchimedean local field of characteristic zero, by using a 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.

R-group, local Langlands correspondence, intertwining operator
Mathematical Subject Classification 2010
Primary: 22E50
Secondary: 11F70
Received: 2 December 2012
Accepted: 5 March 2013
Published: 22 December 2013
Kuok Fai Chao
Shanghai Center for Mathematical Sciences
Fudan University
No. 220 Handan Road
Shanghai, 200433
Wen-Wei Li
Morningside Center of Mathematics
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
55, Zhongguancun East Road
Beijing, 100190