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Depth and the Local Langlands Correspondence

  • Anne-Marie Aubert
  • Paul BaumEmail author
  • Roger Plymen
  • Maarten Solleveld
Chapter
Part of the Progress in Mathematics book series (PM, volume 319)

Abstract

Let G be an inner form of a general linear group over a non-archimedean local field. We prove that the local Langlands correspondence for G preserves depths. We also show that the local Langlands correspondence for inner forms of special linear groups preserves the depths of essentially tame Langlands parameters.

Keywords

Representation theory p-adic group Local Langlands program Division algebra 

2010 Mathematics Subject Classification.

20G25 22E50. 

Notes

Acknowledgements

The authors wish to thank Vincent Sécherre for some helpful explanations on the construction of simple types for GL m (D), Mark Reeder for pointing out some examples where the depth is not preserved, Wilhelm Zink for explaining properties of the Artin reciprocity map and Paul Broussous for providing the reference [BaBr], which has allowed a substantial simplification of the proof of Proposition 2.6 from a previous version. The second author “Paul Baum” was partially supported by NSF grant DMS-1200475.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Anne-Marie Aubert
    • 1
  • Paul Baum
    • 2
    Email author
  • Roger Plymen
    • 3
    • 4
  • Maarten Solleveld
    • 5
  1. 1.Institut de Mathématiques de Jussieu – Paris Rive GaucheU.M.R. 7586 du C.N.R.S., U.P.M.C.ParisFrance
  2. 2.Mathematics DepartmentPennsylvania State UniversityUniversity ParkUSA
  3. 3.School of MathematicsSouthampton UniversitySouthamptonUK
  4. 4.School of MathematicsManchester UniversityManchesterUK
  5. 5.Radboud Universiteit NijmegenNijmegenThe Netherlands

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