## Automorphic forms on GL (2) |

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### Contents

Local Theory 1 Weil representations | 1 |

Representations of GL2F in tne nonarcnimedean case | 23 |

Tne principal series for nonarcnimedean fields | 92 |

Copyright | |

13 other sections not shown

### Common terms and phrases

absolutely convergent absolutely cuspidal admissible representation algebra automorphism belongs character Coker commutative diagram compact complete constituent contains Dedekind domain defined detg direct sum elementary idempotent elements epimorphism equal equivalent exact sequence exists finite dimensional finite groups finite number finite type follows function f functional equation functor Haar measure homomorphism idempotent indecomposable integral invariant subspace irreducible admissible representation irreducible representation K-algebra lattices left R-module Lemma linear Math matrix maximal R-order modules Moreover morphism multiplicative noetherian non-archimedean non-trivial non-zero number field obtain orthogonal polynomial prime ideals principal ideal domain progenerator projective projective resolution proof Proposition prove quasi-character quotient R-module representation of G resp restriction ring satisfies scalar skewfield space of functions splitting field subgroup submodule Suppose theorem theory trace trivial two-sided unique unramified vector verify zero