Advertisement

Israel Journal of Mathematics

, Volume 225, Issue 2, pp 525–551 | Cite as

Restriction of representations of metaplectic GL2(F) to tori

  • Shiv Prakash Patel
  • Dipendra Prasad
Article
  • 41 Downloads

Abstract

Let F be a non-archimedean local field. We study the restriction of irreducible admissible genuine representations of the twofold metaplectic cover \({\widetilde {GL}_2}\) of GL2(F) to the inverse image in \({\widetilde {GL}_2}\) of a maximal torus in GL2(F).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ad03]
    J. Adams, Characters of covering groups of SL(n), Journal of the Institute of Mathematics of Jussieu 2 (2003), 1–21.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [BH06]
    C. J. Bushnell and G. Henniart, The local Langlands Conjecture for GL(2), Grundlehren der Mathematischen Wissenschaften, Vol. 335, Springer-Verlag, Berlin, 2006.Google Scholar
  3. [GPS80]
    S. Gelbart and I. I. Piatetski-Shapiro, Distinguished representations and modular forms of half-integral weight, Inventiones Mathematicae 59 (1980), 145–188.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [GHPS79]
    S. Gelbart, R. Howe and I. Piatetski-Shapiro, Uniqueness and existence of Whittaker models for the metaplectic group, Israel Journal of Mathematics, 34 (1979), 21–37.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [GP92]
    B. H. Gross and D. Prasad, On the decomposition of a representation of SOn when restricted to SOn−1, Canadian Journal of Mathematics, 44 (1992), 974–1002.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [KP84]
    D. A. Kazhdan and S. J. Patterson, Metaplectic forms, Publications Mathématiques. Institut des Hautes Études Scientifiques 59 (1984), 35–142.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [Kub69]
    T. Kubota, On Automorphic Functions and the Reciprocity Law in a Number Field, Lectures in Mathematics, Department of Mathematics, Kyoto University, Vol. 2, Kinokuniya Book-Store Co., Tokyo, 1969.zbMATHGoogle Scholar
  8. [Man84]
    D. Manderscheid, On the supercuspidal representations of SL2 and its two-fold cover. I, II. Mathematische Annalen 266 (1984), 287–295, 297–305.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [MW12]
    C. Moeglin and J.-L. Waldspurger, La conjecture locale de Gross–Prasad pour les groupes spéciaux orthogonaux: le cas général, Astérisque 347 (2012), 167–216.zbMATHGoogle Scholar
  10. [Moe89]
    C. Moen, Kirillov models for distinguished representations, Nagoya Mathematical Journal 116 (1989), 89–110.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [Pat15]
    S. P. Patel, Branching laws for the metaplectic cover of GL2, Pacific Journal of Mathematics 291 (2017), 461–484.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [PP16]
    S. P. Patel and D. Prasad, Multiplicity formula for restriction of representations of \({\widetilde {GL}_2}\) to \({\widetilde {SL}_2}\) , Proceedings of the American Mathematical Society 144 (2016), 903–908.MathSciNetCrossRefGoogle Scholar
  13. [Sai93]
    H. Saito, On Tunnell’s formula for characters of GL(2), Compositio Mathematica 85 (1993), 99–108.MathSciNetzbMATHGoogle Scholar
  14. [Tun83]
    J. B. Tunnell, Local ε-factors and characters of GL(2), American Journal of Mathematics 105 (1983), 1277–1307.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Department of MathematicsBen-Gurion University of the NegevBe’er ShevaIsrael
  2. 2.School of MathematicsTata Institute of Fundamental ResearchColaba, MumbaiIndia

Personalised recommendations