Local Galois Representations

GaloisRepresentation(pi) : RepLoc -> GalRep

WeilRepresentation(pi) : RepLoc -> GalRep

    Precision: RngIntElt                Default: 10

Given a minimal representation π of GL₂(Q_p), this returns the representation ρ_π of the Weil-Deligne group associated to π under the local Langlands correspondence, as a local Galois representation. (See Section The Local Langlands Correspondence and Chapter LOCAL GALOIS REPRESENTATIONS.) In the current implementation, the representation only agrees with ρ_π on inertia.

AdmissiblePair(pi) : RepLoc -> RngPad, Map

Given an ordinary minimal supercuspidal representation π of GL₂(Q_p), this returns the associated admissible pair (E, χ). (See Section The Local Langlands Correspondence.) Two objects are returned: a quadratic field extension E/Q_p, and a map χ which is a character of the unit group of E.