Invariance of 𝑅-groups between 𝑝-adic inner forms of quasi-split classical groups

Choiy, Kwangho; Goldberg, David

doi:10.1090/tran/6485

Invariance of $R$-groups between $p$-adic inner forms of quasi-split classical groups
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Trans. Amer. Math. Soc. 368 (2016), 1387-1410 Request permission

Abstract:

We study the reducibility of parabolically induced representations of non-split inner forms of quasi-split classical groups. The isomorphism of Arthur $R$–groups, endoscopic $R$–groups and Knapp-Stein $R$–groups is established, as well as showing these $R$–groups are isomorphic to the corresponding ones for the quasi-split form. This shows $R$–groups are an invariant of the $L$–packets. The results are applied to classify the elliptic spectrum.

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