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Simple wild -packets

Published online by Cambridge University Press:  16 May 2012

Tasho Kaletha
Tasho Kaletha*
Affiliation:
School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA(tkaletha@math.ias.edu)
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Abstract

In a recent paper, Gross and Reeder study the arithmetic properties of discrete Langlands parameters for semi-simple -adic groups, and they conjecture that a special class of these – the simple wild parameters – should correspond to -packets consisting of simple supercuspidal representations. We provide a construction of this correspondence, and show that the simple wild -packets satisfy many expected properties. In particular, they admit a description in terms of the Langlands dual group, and contain a unique generic element for a fixed Whittaker datum. Moreover, we prove their stability on an open subset of the regular semi-simple elements, and show that they satisfy a natural compatibility with respect to unramified base-change.

Keywords

local Langlands correspondenceL-packetsp-adic groupssupercuspidal representations22E5020G2511S3711F70
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 1 , January 2013 , pp. 43 - 75
Copyright
Copyright © Cambridge University Press 2013

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