nLab
Weil-Deligne representation

Contents

Context

Representation theory

Arithmetic

Contents

Definition

Let

Definition

(Weil-Deligne representation)
A Weil-Deligne representation is a pair (ρ 0,N)(\rho_{0},N) where

and

  • NN is a nilpotent monodromy operator

satisfying

ρ 0(σ)Nρ 0(σ) 1=σN \rho_{0}(\sigma)N\rho_{0}(\sigma)^{-1} \;=\; \left\Vert \sigma \right\Vert N

for all σW F\sigma\in W_{F}.

References

  • John Tate, Section 4 in: Number theoretic background, in: Automorphic forms, representations and L-functions, Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore. (1977), Part 2, Proc. Sympos. Pure Math., XXXIII, pages 3–26. Amer. Math. Soc., Providence, RI (ISBN:978-0-8218-3371-1, pdf, pdf)

  • Robin Zhang, Weil-Deligne Representations I – Local Langlands seminar (pdf, pdf)

Created on April 23, 2021 at 02:20:40. See the history of this page for a list of all contributions to it.