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Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 449–471 | Cite as

On multiplicity in restriction of tempered representations of p-adic groups

  • Kwangho ChoiyEmail author
Article

Abstract

We establish an equality between two multiplicities: one in the restriction of tempered representations of a p-adic group to its closed subgroup with the same derived group; and one occurring in their corresponding component groups in Langlands dual sides, so-called \(\mathcal {S}\)-groups, under working hypotheses about the tempered local Langlands conjecture and the internal structure of tempered L-packets. This provides a formula of the multiplicity for p-adic groups by means of dimensions of irreducible representations of their \(\mathcal {S}\)-groups.

Keywords

Multiplicity in the restriction Local Langlands conjecture Internal structure of L-packet Tempered representation 

Mathematics Subject Classification

Primary 11F70 Secondary 22E50 22E35 

Notes

Acknowledgements

The author would like to express his great appreciation to Tasho Kaletha for his insightful comments and fruitful discussions on this work. He is also grateful to Jeff Adler, Wee Teck Gan, Wen-Wei Li, Dipendra Prasad, and Mark Reeder for their valuable suggestions and helpful communications. The author wishes to thank the referee for a careful reading and many valuable comments and suggestions that have led to improvements in the manuscript. This work was partially done during his visit at Max-Planck-Institut für Mathematik, Bonn in June and July 2016. The author thanks the institute for their generous support and stimulating research environment.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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