On representations of the Weil–Deligne group
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2008), pp. 48-52
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We study admissible orthogonal and symplectic representations of the Weil–Deligne group $\mathcal{W}'(\overline K/K)$ 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 $\mathcal{W}'(\overline K/K)$ is 1.
@article{IVM_2008_2_a6,
author = {M. N. Sabitova},
title = {On representations of the {Weil{\textendash}Deligne} group},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {48--52},
year = {2008},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2008_2_a6/}
}
M. N. Sabitova. On representations of the Weil–Deligne group. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2008), pp. 48-52. http://geodesic.mathdoc.fr/item/IVM_2008_2_a6/
[1] Rohrlich D. E., “Elliptic curves and the Weil-Deligne group”, Elliptic curves and related topics, CRM Proc. Lecture Notes., 4, Amer. Math. Soc., Providence, 1994, 125–157 | MR | Zbl
[2] Deligne P., “Formes modulaires et representations de $\mathrm{GL}(2)$”, Modular functions of one variable, 2, Springer-Verlag, New York, 1973, 55–105 | MR
[3] Deligne P., “Les constantes des équations fonctionnelles des fonctions $L$”, Modular functions of one variable, 2, Springer-Verlag, New York, 1973, 501–595 | MR