A correspondence for the generalized Hecke algebra of the metaplectic cover , -adic.
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Joyner, David (1998)
The New York Journal of Mathematics [electronic only]
Yasuo Morita (1981/1982)
Groupe de travail d'analyse ultramétrique
Magdy Assern (1996)
Manuscripta mathematica
Grassberger, Johannes, Hörmann, Günther (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
Michael G. Cowling, Stefano Meda, Alberto G. Setti (2010)
Colloquium Mathematicae
We give a simple proof of a result of R. Rochberg and M. H. Taibleson that various maximal operators on a homogeneous tree, including the Hardy-Littlewood and spherical maximal operators, are of weak type (1,1). This result extends to corresponding maximal operators on a transitive group of isometries of the tree, and in particular for (nonabelian finitely generated) free groups.
Jeffrey Hakim (1994)
Journal für die reine und angewandte Mathematik
Everling, Ulrich (1998)
The New York Journal of Mathematics [electronic only]
Z. Gong, L. Grenié (2011)
Annales de la faculté des sciences de Toulouse Mathématiques
Given a representation of a local unitary group and another local unitary group , either the Theta correspondence provides a representation of or we set . If is fixed and varies in a Witt tower, a natural question is: for which is ? For given dimension there are exactly two isometry classes of unitary spaces that we denote . For let us denote the minimal of the same parity of such that , then we prove that where is the dimension of .
Francis M. Choucroun (1994)
Mémoires de la Société Mathématique de France
R. J. Plymen, C. W. Leung (1991)
Compositio Mathematica
Fiona Murnaghan (1991)
Compositio Mathematica
Thomas J. Haines (2012)
Annales scientifiques de l'École Normale Supérieure
Let be an unramified group over a -adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with -level structure initiated by M. Rapoport and the author in [15].
Sami Mustapha (2006)
Annales de l'I.H.P. Probabilités et statistiques
Fiona Murnaghan (1996)
Annales scientifiques de l'École Normale Supérieure
Chris Jantzen (1993)
Journal für die reine und angewandte Mathematik
Ju-Lee Kim (2004)
Bulletin de la Société Mathématique de France
Let be a -adic field. Let be the group of -rational points of a connected reductive group defined over , and let be its Lie algebra. Under certain hypotheses on and , wequantifythe tempered dual of via the Plancherel formula on , using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on and . As a consequence, we prove that any tempered representation contains a good minimal -type; we extend this result to irreducible...
Jean-Loup Waldspurger (2009)
Annales de l’institut Fourier
La stabilisation de la formule des traces utilise non seulement le “lemme fondamental”, mais aussi plusieurs variantes dont l’une est le “lemme fondamental pondéré”. Nous montrons que, si celui-ci est vrai sur un corps de base de caractéristique positive, il l’est aussi sur un corps de base de caractéristique nulle. Pour cela, nous introduisons un certain espace de fonctions contenant les fonctions caractéristiques des réseaux de Moy-Prasad. Nous montrons que les intégrales orbitales pondérées des...
Marie-France Vignéras (1996)
Compositio Mathematica
Burt Totaro (1999)
Publications Mathématiques de l'IHÉS
Yehuda Shalom (2000)
Annales de l'institut Fourier
Consider a simple non-compact algebraic group, over any locally compact non-discrete field, which has Kazhdan’s property . For any such group, , we present a Kazhdan set of two elements, and compute its best Kazhdan constant. Then, settling a question raised by Serre and by de la Harpe and Valette, explicit Kazhdan constants for every lattice in are obtained, for a “geometric” generating set of the form , where is a ball of radius , and the dependence of on is described explicitly....
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