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On \(L\)-Packets for Inner Forms of \(SL_n\)
Kaoru Hiraga, Kyoto University, Japan, and Hiroshi Saito
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Memoirs of the American Mathematical Society
2011; 97 pp; softcover
Volume: 215
ISBN-10: 0-8218-5364-3
ISBN-13: 978-0-8218-5364-1
List Price: US$70
Individual Members: US$42
Institutional Members: US$56
Order Code: MEMO/215/1013
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The theory of \(L\)-indistinguishability for inner forms of \(SL_2\) has been established in the well-known paper of Labesse and Langlands (L-indistinguishability for SL\((2)\). Canad. J. Math. 31 (1979), no. 4, 726-785).

In this memoir, the authors study \(L\)-indistinguishability for inner forms of \(SL_n\) for general \(n\). Following the idea of Vogan in (The local Langlands conjecture. Representation theory of groups and algebras, 305-379, Contemp. Math. 145 (1993)), they modify the \(S\)-group and show that such an \(S\)-group fits well in the theory of endoscopy for inner forms of \(SL_n\).

Table of Contents

  • Introduction
  • Restriction of representations
  • Whittaker normalization over local fields
  • Restriction of cusp forms
  • Whittaker normalization over global fields
  • Endoscopy and its automorphisms
  • A conjectural formula for endoscopic transfer
  • Descent to Levi subgroups
  • Relevance conditions for Langlands parameters
  • Endoscopy for inner forms of \(GL_n\)
  • Local Langlands correspondence for inner forms of \(GL_n\)
  • \(L\)-packets for inner forms of \(SL_n\)
  • \(L\)-packets for inner forms of \(SL_n\) over Archimedean fields
  • Multiplicity formula for \(SL_n\)
  • Multiplicity formula for inner forms of \(SL_n\)
  • Lemmas for trace formula
  • Trace formula
  • Transfer factors
  • Bibliography
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