## Lecture Notes in Mathematics, Volume 166 |

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### Contents

LIBRAW | 1 |

A DESCRIPTION OF ALL IRREDUCIBLE REPRESENTATIONS OF K PGL20 | 2 |

THE IRREDUCIBLE UNITARY REPRESENTATIONS OF PGL2fi AND THEIR CHARACTERS | 36 |

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### Common terms and phrases

AflK algebraically irreducible representation Assume Chapter compact support compute conductor conjugacy classes Corollary correspond decomposes simply decomposition denote direct sum double cosets equation equivalent explicit finite finite-dimensional follows Fourier transform functions on G g e G Haar measure Hilbert space homomorphism implies induced representation inequivalent integral inversion formula irreducible repre irreducible unitary representation isomorphism K-module lemma mapping matrix coefficients Mautner multiplicative character non-regular elements norm occurs in res operator ord(b ord(c orthogonal orthonormal base Plancherel's formula primitive mod primitive mod pm principal series Proof quadratic extension ramified real-valued reducible mod representations of G res T contains res T decomposes restrictions Schur orthogonality relations Seiten sentation series of G space H spherical functions subspace TflK Theorem 3.3 trace unique unramified discrete series vector space write