منابع مشابه
On the Local Langlands Correspondence
The local Langlands correspondence for GL(n) of a non-Archimedean local field F parametrizes irreducible admissible representations of GL(n, F ) in terms of representations of the Weil-Deligne group WDF of F . The correspondence, whose existence for p-adic fields was proved in joint work of the author with R. Taylor, and then more simply by G. Henniart, is characterized by its preservation of s...
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We show that local-global compatibility (at split primes) away from p holds at all points of the p-adic eigenvariety of a definite n-variable unitary group. The novelty is we allow non-classical points, possibly non-étale over weight space. More precisely we interpolate the local Langlands correspondence for GLn across the eigenvariety by considering the fibers of its defining coherent sheaf. W...
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In these notes, based on my lectures at the FRG workshop on “Characters, Liftings, and Types” at American University in June 2012, I give an introduction to the conjectural Local Langlands Correspondence (LLC), for split semisimple groups over a nonarchimedean local field. This conjecture has been evolving over the past 45 years (with roots going back much further) to the point that today’s sta...
متن کاملOn the Langlands correspondence for symplectic motives
In this paper, we present a refinement of the global Langlands correspondence for discrete symplectic motives of rank 2n over Q. To such a motive Langlands conjecturally associates a generic, automorphic representation π of the split orthogonal group SO2n+1 over Q, which appears with multiplicity one in the cuspidal spectrum. Using the local theory of generic representations of odd orthogonal g...
متن کاملTwisted Geometric Langlands Correspondence for a Torus
Let T be a split torus over local or global function field. The theory of BrylinskiDeligne gives rise to the metaplectic central extensions of T by a finite cyclic group. The representation theory of these metaplectic tori has been developed to some extent in the works of M. Weissman, G. Savin, W. T. Gan, P. McNamara and others. In this paper we propose a geometrization of this theory in the fr...
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ژورنال
عنوان ژورنال: Transactions of the Moscow Mathematical Society
سال: 2018
ISSN: 0077-1554,1547-738X
DOI: 10.1090/mosc/278