THE LANGLANDS-SHAHIDI METHOD FOR PAIRS VIA TYPES AND COVERS

Yeongseong Jo, M. Krishnamurthy

Research output: Contribution to journalArticlepeer-review

Abstract

We compute the local coefficient attached to a pair (π1, π2) of supercuspidal (complex) representations of the general linear group using the theory of types and covers ‘a la Bushnell-Kutzko. In the process, we obtain another proof of a well-known formula of Shahidi for the corresponding Plancherel constant. The approach taken here can be adapted to other situations of arithmetic interest within the context of the Langlands-Shahidi method, particularly to that of a Siegel Levi subgroup inside a classical group.

Original languageEnglish
Pages (from-to)635-672
Number of pages38
JournalRepresentation Theory
Volume26
DOIs
StatePublished - 2022

Bibliographical note

Funding Information:
The first author would like to thank R. Ye and E. Zelingher for a very helpful discussion about the choice of the additive character. The second author would like to thank Phil Kutzko for many helpful discussions regarding this paper. Finally, we thank the anonymous referee for their useful comments.

Publisher Copyright:
© 2022. American Mathematical Society

Keywords

  • epsilon factors
  • local coefficients
  • Types and covers

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