Abstract
Let G be a quasisplit reductive group over a p-adic field k, T a maximal unramified anisotropic torus ofG.k/, and a character ofT.k/ satisfying certain conditions. Assume the residue characteristicp ofk is large enough. It was shown by DeBacker and Reeder that the irreducible supercuspidal representation of G.k/ associated to .T.k/;/ is generic if and only if B.T;k/ is a special vertex of B.G;k/. We compute the set of maximal nilpotent support Nwh;max. / when B.T;k/ is not a special point in B.G;k/.
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