Invariant representations of GSp(2) under tensor product with a quadratic character
著者
書誌事項
Invariant representations of GSp(2) under tensor product with a quadratic character
（Memoirs of the American Mathematical Society, no. 957）
American Mathematical Society, c2009
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注記
"Volume 204, number 957 (first of 5 numbers)."
Includes bibliographical references (p. 163-165) and index
内容説明・目次
内容説明
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)
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