## Harmonic Analysis on Reductive P-adic Groups |

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### Contents

Existence of characters for the discrete series JJBRAW | 4 |

Existence of characters in the general case | 12 |

Supercusp forms and supercuspidal representations | 20 |

Copyright | |

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### Common terms and phrases

A+(t Ad(Y adic groups algebraic varieties assume Cartan subgroup compact mod compact set compact subset compact support completes the proof Conjecture Corollary cuspidal pair cuspidal representations defined det(t dim G elements finite subset following property Furthermore G-orbit Haar measure Harish-Chandra Hence holomorphic invariant irreducible K-finite Lemma Lemma 19 Lemma 28 Let f Let G Lie algebra linear locally compact locally constant functions locally summable mapping Math maximal split torus open compact subgroup open neighborhood parabolic subgroup proof of Lemma proof of Theorem proves the lemma reductive remains bounded representation of G Seiten Seminar semisimple Lie groups space split component subgroup of G subset of G subspace supercusp form Supp f Theorem Theorem 13 Theory uA+(c unipotent radical unitary representation x c G x e G x t G