Abstract
We study admissible orthogonal and symplectic representations of the Weil-Deligne group W′(\( \overline K \)/K) of a local non-Archimedean field K. As an application of the obtained results we show that the root number of the tensor product of two admissible symplectic representations of W′(\( \overline K \)/K) is 1.
This is a preview of subscription content, log in via an institution to check access.
References
D. E. Rohrlich, “Elliptic Curves and the Weil-Deligne Group,” in Elliptic Curves and Related Topics. CRM Proc. Lecture Notes (Providence, Amer. Math. Soc., 1994, Vol. 4), pp. 125–157.
P. Deligne, “Formes Modulaires et Représentations de GL(2),” in Modular Functions of One Variable (Springer-Verlag, New York, 1973, Vol. 2), pp. 55–105.
P. Deligne, “Les Constantes des Équations Fonctionnelles des Fonctions L,” in Modular Functions of One Variable (Springer-Verlag, New York, 1973, Vol. 2), pp. 501–595.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.N. Sabitova, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 2, pp. 48–52.
About this article
Cite this article
Sabitova, M.N. On representations of the Weil-Deligne group. Russ Math. 52, 46–50 (2008). https://doi.org/10.3103/S1066369X08020072
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X08020072