Local Galois Representations

GaloisRepresentation(pi): RepLoc → GalRep

WeilRepresentation(pi): RepLoc → GalRep

Precision : RngIntElt                    Default: 10

Given a minimal representation \(\pi\) of \({\operatorname{GL}}_2({\mathbb{Q}}_p),\) this returns the representation \(\rho_\pi\) of the Weil-Deligne group associated to \(\pi\) under the local Langlands correspondence, as a local Galois representation. (See Section The Local Langlands Correspondence and Chapter galrep.) In the current implementation, the representation only agrees with \(\rho_\pi\) on inertia.

AdmissiblePair(pi): RepLoc → RngPad, Map

Given an ordinary minimal supercuspidal representation \(\pi\) of \({\operatorname{GL}}_2({\mathbb{Q}}_p),\) this returns the associated admissible pair \((E,\chi).\) (See Section The Local Langlands Correspondence.) Two objects are returned: a quadratic field extension \(E/{\mathbb{Q}}_p\), and a map \(\chi\) which is a character of the unit group of \(E.\)