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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Geometric Waldspurger periods II
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by Sergey Lysenko PDF
Represent. Theory 24 (2020), 235-291 Request permission

Abstract:

In this paper we extend the calculation of the geometric Waldspurger periods from our paper [Compos. Math. 144 (2008), no. 2, 377–438] to the case of ramified coverings. We give some applications to the study of Whittaker coeffcients of the theta-lifting of automorphic sheaves from $\operatorname {PGL}_2$ to the metaplectic group $\widetilde {\operatorname {SL}}_2$; they agree with our conjectures from [Geometric Whittaker models and Eisenstein series for $\mathrm {Mp}_2$, arXiv:1221.1596]. In the process of the proof, we construct some new automorphic sheaves for ${\operatorname {GL}_2}$ in the ramified setting. We also formulate stronger conjectures about Waldspurger periods and geometric theta-lifting for the dual pair $(\widetilde {\operatorname {SL}}_2, \operatorname {PGL}_2)$.
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Additional Information
  • Sergey Lysenko
  • Affiliation: Institut Elie Cartan Lorraine, Université de Lorraine, B.P. 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France
  • MR Author ID: 614865
  • Email: Sergey.Lysenko@univ-lorraine.fr
  • Received by editor(s): September 9, 2019
  • Received by editor(s) in revised form: May 15, 2020
  • Published electronically: July 2, 2020
  • Additional Notes: The author was supported by the ANR program ANR-13-BS01-0001-01.
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 235-291
  • MSC (2010): Primary 11R39; Secondary 14H60
  • DOI: https://doi.org/10.1090/ert/543
  • MathSciNet review: 4127907