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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Multiplicity formula for restriction of representations of $\widetilde {\mathrm {GL}_{2}}(F)$ to $\widetilde {\mathrm {SL}_{2}}(F)$
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by Shiv Prakash Patel and Dipendra Prasad PDF
Proc. Amer. Math. Soc. 144 (2016), 903-908 Request permission

Abstract:

In this note we prove a certain multiplicity formula regarding the restriction of an irreducible admissible genuine representation of a 2-fold cover $\widetilde {\mathrm {GL}}_{2}(F)$ of $\mathrm {GL}_{2}(F)$ to the 2-fold cover $\widetilde {\mathrm {SL}}_{2}(F)$ of $\mathrm {SL}_{2}(F)$, and find in particular that this multiplicity may not be one, a result that was recently observed for certain principal series representations in the work of Szpruch (2013). The proofs follow the standard path via Waldspurger’s analysis of theta correspondence between $\widetilde {\mathrm {SL}}_{2}(F)$ and $\textrm {PGL}_{2}(F)$.
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Additional Information
  • Shiv Prakash Patel
  • Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
  • Email: shiv@math.iitb.ac.in
  • Dipendra Prasad
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
  • MR Author ID: 291342
  • Email: dprasad@math.tifr.res.in
  • Received by editor(s): September 10, 2014
  • Received by editor(s) in revised form: December 31, 2014
  • Published electronically: May 28, 2015
  • Communicated by: Kathrin Bringmann
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 903-908
  • MSC (2010): Primary 22E35; Secondary 22E50
  • DOI: https://doi.org/10.1090/proc12721
  • MathSciNet review: 3430864