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ON THE LOCAL LANGLANDS CORRESPONDENCE FOR SPLIT CLASSICAL GROUPS OVER LOCAL FUNCTION FIELDS

Part of: Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  30 September 2015

Radhika Ganapathy  and
Sandeep Varma
Radhika Ganapathy
Affiliation:
Department of Mathematics, The University of British Columbia, Vancouver, Canada ([email protected])
Sandeep Varma
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, India ([email protected])
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Abstract

We prove certain depth bounds for Arthur’s endoscopic transfer of representations from classical groups to the corresponding general linear groups over local fields of characteristic 0, with some restrictions on the residue characteristic. We then use these results and the method of Deligne and Kazhdan of studying representation theory over close local fields to obtain, under some restrictions on the characteristic, the local Langlands correspondence for split classical groups over local function fields from the corresponding result of Arthur in characteristic 0.

Keywords

local Langlands correspondenceclose local fieldsendoscopy

MSC classification

Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 5 , November 2017 , pp. 987 - 1074
Copyright
© Cambridge University Press 2015 

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