## Lecture Notes in Mathematics, Volume 166 |

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Page 96

We call an irreducible representation u of K

integer for which u may be considered as a representation of K1. To list all

irreducible representations of K it is sufficient to list all those which are

We call an irreducible representation u of K

**primitive mod**Pi if i 1b the leastinteger for which u may be considered as a representation of K1. To list all

irreducible representations of K it is sufficient to list all those which are

**primitive****mod**P1 for ...Page 97

The representations which are

remarks: 1) Degrees of representations which are

the irreducible representations of the principal series of K which are

The representations which are

**primitive mod**for i >_ 2: We begin with someremarks: 1) Degrees of representations which are

**primitive mod**P : For any 1 > 1the irreducible representations of the principal series of K which are

**primitive****mod**P ...Page 100

q1"2(q-l) (i+D /2<J<i Category representations of the ramified discrete series of K,

indexed by characters * which are

representations u indexed by characters ir,i ir which are

q1"2(q-l) (i+D /2<J<i Category representations of the ramified discrete series of K,

indexed by characters * which are

**primitive mod**p »* □ it or n~ u if and only ifrepresentations u indexed by characters ir,i ir which are

**primitive mod**p^*, ...### What people are saying - Write a review

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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 |

Copyright | |

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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