eBook ISBN:  9781470405717 
Product Code:  MEMO/204/957.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470405717 
Product Code:  MEMO/204/957.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 204; 2009; 172 ppMSC: Primary 11
Let \(F\) be a number field or a \(p\)adic field. The author introduces in Chapter 2 of this work two reductive rank one \(F\)groups, \(\mathbf{H_1}\), \(\mathbf{H_2}\), which are twisted endoscopic groups of \(\mathrm{GSp}(2)\) with respect to a fixed quadratic character \(\varepsilon\) of the idèle class group of \(F\) if \(F\) is global, \(F^\times\) if \(F\) is local. When \(F\) is global, Langlands functoriality predicts that there exists a canonical lifting of the automorphic representations of \(\mathbf{H_1}\), \(\mathbf{H_2}\) to those of \(\mathrm{GSp}(2)\). In Chapter 4, the author establishes this lifting in terms of the Satake parameters which parameterize the automorphic representations. By means of this lifting he provides a classification of the discrete spectrum automorphic representations of \(\mathrm{GSp}(2)\) which are invariant under tensor product with \(\varepsilon\).

Table of Contents

Chapters

1. Introduction

2. $\varepsilon $Endoscopy for $\textup {GSp}(2)$

3. The Trace Formula

4. Global Lifting

5. The Local Picture

A. Summary of Global Lifting

B. Fundamental Lemma


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Let \(F\) be a number field or a \(p\)adic field. The author introduces in Chapter 2 of this work two reductive rank one \(F\)groups, \(\mathbf{H_1}\), \(\mathbf{H_2}\), which are twisted endoscopic groups of \(\mathrm{GSp}(2)\) with respect to a fixed quadratic character \(\varepsilon\) of the idèle class group of \(F\) if \(F\) is global, \(F^\times\) if \(F\) is local. When \(F\) is global, Langlands functoriality predicts that there exists a canonical lifting of the automorphic representations of \(\mathbf{H_1}\), \(\mathbf{H_2}\) to those of \(\mathrm{GSp}(2)\). In Chapter 4, the author establishes this lifting in terms of the Satake parameters which parameterize the automorphic representations. By means of this lifting he provides a classification of the discrete spectrum automorphic representations of \(\mathrm{GSp}(2)\) which are invariant under tensor product with \(\varepsilon\).

Chapters

1. Introduction

2. $\varepsilon $Endoscopy for $\textup {GSp}(2)$

3. The Trace Formula

4. Global Lifting

5. The Local Picture

A. Summary of Global Lifting

B. Fundamental Lemma