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On Stability and Endoscopic Transfer of Unipotent Orbital Integrals on \(p\)-adic Symplectic Groups
Magdy Assem
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Memoirs of the American Mathematical Society
1998; 101 pp; softcover
Volume: 134
ISBN-10: 0-8218-0765-X
ISBN-13: 978-0-8218-0765-1
List Price: US$46
Individual Members: US$27.60
Institutional Members: US$36.80
Order Code: MEMO/134/635
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The theory of endoscopy is an intriguing part of the Langlands program, as it provides a way to attack the functoriality principle of Langlands for certain pairs of reductive groups \((G,H)\), in which \(H\) is what is known as an endoscopic group for \(G\). The starting point for this method is a close study of the relationship of orbital integrals on \(G\) with stable orbital integrals on \(H\).

This volume investigates unipotent orbital integrals of spherical functions on \(p\)-adic symplectic groups. The results are then put into a conjectural framework, that predicts (for split classical groups) which linear combinations of unipotent orbital integrals are stable distributions.

Readership

Research mathematicians interested in analysis on \(p\)-adic Lie groups.

Table of Contents

  • Introduction
  • Unipotent orbits and prehomogeneous spaces
  • The Hecke algebra and some Igusa local orbital zeta functions
  • The evaluation of \(f^H\) at the identity
  • Matching of unipotent orbital integrals
  • Remarks on stability and endoscopic transfer
  • Appendix I
  • Appendix II
  • References
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