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Calculs de facteurs epsilon de paires sur un corps local, II

Published online by Cambridge University Press:  04 December 2007

Colin J. Bushnell
Affiliation:
Department of Mathematics, King's College, Strand, London WC2R 2LS, U.K. E-mail: bushnell@mth.kcl.ac.uk
Guy Henniart
Affiliation:
Département de Mathématiques & UMR 8628 du CNRS, Bâtiment 425, Université de Paris-Sud, 91405 Orsay cedex, France. E-mail: Guy.Henniart@math.u-psud.fr
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Abstract

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Let F a locally compact non-Archimedean field, of residue characteristic p, and ψ a nontrivial additive character of F. Let σ, σ′ be irreducible representations of the absolute Weil group of F, each of degree a power of p and not induced from a nontrivial unramified extension of F. We give a formula for the value at $s=½ of the ϵ-factor ϵ (σ ⊗ σ ',ψ,s)$, modulo roots of unity in ${\Bbb C}$ of order a power of p. Via the Langlands correspondence, we get an analogous formula for supercuspidal representations of ${\rm GL}_n(F)$.

Type
Research Article
Copyright
© 2000 Kluwer Academic Publishers
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