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

Conference paper

DOI: 10.1007/978-3-319-17987-2_4

Volume 2 of the book series Association for Women in Mathematics Series (AWMS)
Cite this paper as:
David A., Hanzer M., Ludwig J. (2015) 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. In: Bertin M., Bucur A., Feigon B., Schneps L. (eds) Women in Numbers Europe. Association for Women in Mathematics Series, vol 2. Springer, Cham

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.

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