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Gamma-functions of representations and lifting | | Alexander Braverman
; David Kazhdan
; V. Vologodsky
; | | Date: |
28 Dec 1999 | | Subject: | Algebraic Geometry; Representation Theory; Number Theory | math.AG math.NT math.RT | | Abstract: | Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual group of F one can associate certain meromorphic function on the set of isomorphism classed of irreducible representations of G (which we call gamma-functions). In this paper we describe a general framework for an explicit construction of these gamma-functions. We make this idea precise in certain special cases. As a byproduct we give explicit conjectural formulas for the representation $l_E( heta)$ of the group GL(n,F) associated to a character $ heta$ of the multiplicative group $E^*$ of a separable extension E of F of degree n. We also describe a conjectural analogue of the Poisson summation formula associated to a representation of the Langlands dual group, which implies the existence of the meromorphic continuation and functional equation for the corresponding automorphic L-functions. | | Source: | arXiv, math.AG/9912208 | | Services: | Forum | Review | PDF | Favorites | |
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