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Invariant Representations of \(\mathrm{GSp}(2)\) under Tensor Product with a Quadratic Character
Ping-Shun Chan, Ohio State University, Columbus, OH

Memoirs of the American Mathematical Society
2009; 172 pp; softcover
Volume: 204
ISBN-10: 0-8218-4822-4
ISBN-13: 978-0-8218-4822-7
List Price: US$81
Individual Members: US$48.60
Institutional Members: US$64.80
Order Code: MEMO/204/957
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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 \(\varepsilon\).

Table of Contents

  • Introduction
  • \(\varepsilon\)-endoscopy for \(\mathrm{GSp}(2)\)
  • The trace formula
  • Global lifting
  • The local picture
  • Appendix A. Summary of global lifting
  • Appendix B. Fundamental lemma
  • Bibliography
  • List of symbols
  • Index
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