On tori periods of Weil representations of unitary groups

• Neelima Borade ^[1] ; Jonas Franzel ^[2] ; Johannes Girsch ^[5] ; Wei Yao ^[6] ; Qiyao Yu ^[3] ; Elad Zelingher ^[4]
  1. [1] Princeton University

     Princeton University

     Estados Unidos

     
  2. [2] University of Duisburg-Essen

     University of Duisburg-Essen

     Kreisfreie Stadt Essen, Alemania

     
  3. [3] Columbia University

     Columbia University

     Estados Unidos

     
  4. [4] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
  5. [5] University of Sheffield,United Kingdo
  6. [6] University Ave, Chicago, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01047-4
• Enlaces
  • Texto completo
• Resumen

  • We determine the restriction of Weil representations of unitary groups to maximal tori. In the local case, we show that the Weil representation contains a pair of compatible characters if and only if a root number condition holds. In the global case, we show that a torus period corresponding to a maximal anisotropic torus of the global theta lift of a character does not vanish if and only if the local condition is satisfied everywhere and a central value of an L-function does not vanish. Our proof makes use of the seesaw argument and of the well-known theta lifting results from U(1) to U(1). Our results are used in [1, 2] to construct Arthur packets for G2.

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