One of the major achievements of Harish-Chandra was a derivation of the Plancherel formula for real and p-adic groups [9,10]. To have an explicit formula, one will have to compute the measures appearing in the formula; the so called Plancherel measures and formal degrees [12]. (For reasons stemming from L-indistinguishability, we would like to distinguish between the formal degrees for discrete series and the Plancherel measures for non-discrete tempered representations, cf. Proposition 9.3 of [29].) While for real groups the Plancherel measures are completely understood [1, 9, 22], until recently little was known in any generality for p-adic groups [29] (except for their rationality and general form due to Silberger [39]). On the other hand any systematic study of the non-discrete tempered spectrum of a p-adic group would very likely have to follow the path of Knapp and Stein [20, 21] and their theory of 72-groups. Since the basic reducibility theorems for p-adic groups are available [40, 41], it is the knowledge of Plancherel measures which would be necessary to determine the R-groups. This is particularly evident from the important and the fundamental work of Keys [16, 17, 18] and the work of the author [29, 30, 31].

Langlands’ Conjecture on Plancherel Measures for p-Adic Groups

© Bulletin de la S. M. F., 1992, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http: //smf.emath.fr/Publications/Bulletin/Presentation.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/ conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

/pdf/distinguished-representations-and-a-fourier-summation-5edl7lj6ie.pdf

Distinguished representations and a Fourier summation formula

We determine the reducibility and number of components of any representation of a quasi-split unitary group which is parabolically induced from a discrete series representation. The R-groups are computed explicitly, in terms of reducibility for maximal parabolics. This gives a description of the elliptic representations.

/pdf/r-groups-and-elliptic-representations-for-unitary-groups-1dhy3tcg9z.pdf

$R$-groups and elliptic representations for unitary groups

Reducibility for non-connected $p$-adic groups, with $Gsp circ$ of prime index

Induced representations of U (2,2) over a p-adic field

© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1987, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www. elsevier.com/locate/ansens) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

/pdf/l-indistinguishability-and-r-groups-for-quasisplit-groups-g0y6jau9oe.pdf

$L$ -indistinguishability and $R$ -groups for quasisplit groups : unitary groups in even dimension

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$L$ -indistinguishability and $R$ -groups for quasisplit groups : unitary groups in even dimension