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The Conjectural Relation Between Generalized Shalika Models on \(\mathop{\mathrm{SO}}\nolimits _{4n}(F)\) and Symplectic Linear Models on \(\mathop{\mathrm{Sp}}\nolimits _{4n}(F)\): A Toy Example

  • Agnès David
  • Marcela Hanzer
  • Judith Ludwig
Conference paper
Part of the Association for Women in Mathematics Series book series (AWMS, volume 2)

Abstract

We show that if an irreducible admissible representation of \(\mathop{\mathrm{SO}}\nolimits _{4}(F)\) has a generalized Shalika model, its theta lift to \(\mathop{\mathrm{Sp}}\nolimits _{4}(F)\) is non-zero and has a symplectic linear model.

Notes

Acknowledgements

This project started at the WIN-Europe conference in October 2013. We would like to thank the organizers of the conference and the CIRM in Luminy for providing such excellent working conditions. We are grateful to the referee for several helpful comments. MH has been supported in part by the Croatian Science Foundation under the project 9364. JL would like to thank Imperial College London for providing financial support in form of a Doris Chen Mobility Award.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Mathematical Research UnitUniversity of LuxembourgLuxembourgLuxembourg
  2. 2.Department of MathematicsUniversity of ZagrebZagrebCroatia
  3. 3.Mathematical InstituteUniversity of BonnBonnGermany

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