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Gamma factors, root numbers, and distinction

  • Nadir Matringe,
    Laboratoire de Mathématiques et Applications Téléport 2-BP 30179, 11 Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France
  • Omer Offen,
    Department of Mathematics, Technion, Israel Institute of Technology , Haifa 3200003, Israel
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Abstract

We study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of $p$-adic fields. We show that the local Rankin-Selberg root number of any pair of distinguished representation is trivial and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at $1/2$ is trivial for distinguished representations as well as the converse problem.
Keywords: distinguished representation, local constant distinguished representation, local constant
MSC Classifications: 11F70 show english descriptions Representation-theoretic methods; automorphic representations over local and global fields 11F70 - Representation-theoretic methods; automorphic representations over local and global fields
 

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