An Introduction to Langlands Program

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39814 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Pournaki, Mohammadreza
Abstract:
The Weil group WF is assigne to every local field F. Langlands Correspondence is a bijetion between semisimple two-dimensional Deligne representations of Weil Group WF and irreducible representations of GL2(F) which fixes assigned L-functions and local constants. In this thesis we have classified an important class of irreducible representations of GL(2) over local fields called Principal Series. We also tried to give a taste of Langlands Correspondence to the reader. First we explain preliminaries and introduce locally profinite groups and their smooth representations. Then we classify representations of GL2(F) when F is finite. Then we study GL2(F) when F is a local field. Finally we introduce Weil groups and theire semisimple Deligne represntations, and explain the Langlands Correspondence for GL(2).
Keywords:
Locally Profinite Group ; Frobenius Reciprocity ; Smooth Representations ; Weil Group ; L-Function ; Langlands Correspondence

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