Invariant representations of GSp(2) under tensor product with a quadratic character / Ping-Shun Chan.

Format:

Book

Author/Creator:

Chan, Ping-Shun, 1978- author.

Series:

Memoirs of the American Mathematical Society ; Volume 204, Number 957.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 204, Number 957

Language:

English

Subjects (All):

Automorphisms.

Spectral theory (Mathematics).

Tensor products.

p-adic analysis.

Physical Description:

1 online resource (172 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2009.

Language Note:

English

Summary:

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 $\textup{GSp}(2)$ with respect to a fixed quadratic character $\varepsilon$ of the idele 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 $\textup{GSp}(2)$. 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 $\textup{GSp}(2)$ which are invariant under tensor product with $\varepsilon$. Table of Contents: Introduction; $\varepsilon$-endoscopy for $\textup{GSp}(2)$; The trace formula; Global lifting; The local picture; Appendix A. Summary of global lifting; Appendix B. Fundamental lemma; Bibliography; List of symbols; Index. (MEMO/204/957)

Contents:

""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""1.1. An Overview""; ""1.2. -Invariant Automorphic Representations""; ""1.3. Local Character Identities""; ""1.4. Statement of Main Results""; ""1.5. Acknowledgments""; ""Chapter 2. -Endoscopy for GSp(2)""; ""2.1. Endoscopic Data""; ""2.2. Endoscopic group H1""; ""2.3. Endoscopic group H2""; ""2.4. Norm Correspondence""; ""2.5. Matching Functions""; ""Chapter 3. The Trace Formula""; ""3.1. The Fine -Expansion""; ""3.2. Comparison of the Geometric Sides of Trace Formulas""; ""3.3. Application of the Kottwitz-Shelstad Formula""

""Chapter 4. Global Lifting""""4.1. The -Trace Identity""; ""4.2. Frobenius-Hecke Classes""; ""4.3. Packets""; ""4.4. Contributions""; ""4.5. Some Global Lifting Results""; ""4.6. Final Words""; ""Chapter 5. The Local Picture""; ""5.1. Parabolically Induced Representations""; ""5.2. Parabolically Induced Representations

-Split Case""; ""5.3. Character Identities for Unstable Packets""; ""5.4. Character Identities for Stable Packets""; ""Appendix A. Summary of Global Lifting""; ""A.1. Unstable (quasi-)packets of G""; ""A.2. Stable (quasi-)packets""; ""A.3. Induced representations""

""Appendix B. Fundamental Lemma""""B.1. Norm Correspondence

-Elliptic Elements""; ""B.2. Comparison of Orbital Integrals""; ""Bibliography""; ""List of Symbols""; ""Index""

Notes:

"Volume 204, Number 957 (first of 5 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0571-7