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Local Galois Representations

GaloisRepresentation(pi) : RepLoc -> GrpPerm, Map, RngPad, ModGrp
WeilRepresentation(pi) : RepLoc -> GrpPerm, Map, RngPad, ModGrp
    Precision: RngIntElt                Default: 10
Given a minimal representation πof GL2(Qp), this returns the representation of the Weil group associated to πunder the local Langlands correspondence. (See Section The Local Langlands Correspondence.)

More precisely, the objects returned are G, α, L and ρ. L/Qp is a finite Galois extension which the representation factors through, G is an abstract group and αis a bijective map identifying G with Gal(L/Qp), and ρis a G-module. In this way ρdescribes the Weil representation on Gal(L/Qp).

(See Chapter K[G]-MODULES AND GROUP REPRESENTATIONS for information about group modules in Magma.)

AdmissiblePair(pi) : RepLoc -> RngPad, Map
Given an ordinary minimal supercuspidal representation πof GL2(Qp), this returns the associated admissible pair (E, chi). (See Section The Local Langlands Correspondence.) Two objects are returned: a quadratic field extension E/Qp, and a map chi which is a character of the unit group of E.
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013