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Structure of Admissible Representations

IsPrincipalSeries(pi) : RepLoc -> BoolElt
This is true iff the admissible representation πbelongs to the principal series.
IsSupercuspidal(pi) : RepLoc -> BoolElt
This is true iff the admissible representation πis supercuspidal.
PrincipalSeriesParameters(pi) : RepLoc -> GrpDrchElt, GrpDrchElt
Given a principal series representation πof GL2(Qp), this returns two Dirichlet characters of p-power conductor which represent the restriction to Zp x x Zp x of the character of the split torus of GL2(Qp) associated to π.
CuspidalInducingDatum(pi) : RepLoc -> ModGrp
Given a minimal supercuspidal representation πof GL2(Qp), this returns a cuspidal inducing datum that gives rise to π.

Recall (from Section Supercuspidal Representations) that a cuspidal inducing datum (K, Ξ) consists of a subgroup K of GL2(Qp) and a representation Ξof K that gives rise to πvia induction. Importantly, Ξfactors through some finite quotient K/K1 of K. This function returns such a representation of K/K1. From this one can deduce the representation on K, and hence π.

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012