Invariant Representations of GSp(2) Under Tensor Product with a Quadratic Character (Memoirs of the American Mathematical Society v. 204, No. 957)

Invariant Representations of GSp(2) Under Tensor Product with a Quadratic Character (Memoirs of the American Mathematical Society v. 204, No. 957)

By: Ping-Shun Chan (author)Paperback

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Description

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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Product Details

  • publication date: 15/03/2010
  • ISBN13: 9780821848227
  • Format: Paperback
  • Number Of Pages: 172
  • ID: 9780821848227
  • ISBN10: 0821848224

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