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On $L$-Packets for Inner Forms of $SL_n$
 
Kaoru Hiraga Kyoto University, Kyoto, Japan
On $L$-Packets for Inner Forms of $SL_n$
eBook ISBN:  978-0-8218-8519-2
Product Code:  MEMO/215/1013.E
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
On $L$-Packets for Inner Forms of $SL_n$
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On $L$-Packets for Inner Forms of $SL_n$
Kaoru Hiraga Kyoto University, Kyoto, Japan
eBook ISBN:  978-0-8218-8519-2
Product Code:  MEMO/215/1013.E
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2152011; 97 pp
    MSC: Primary 22; Secondary 11;

    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
     
     
    • Chapters
    • 1. Introduction
    • 2. Restriction of Representations
    • 3. Whittaker Normalization over Local Fields
    • 4. Restriction of Cusp Forms
    • 5. Whittaker Normalization over Global Fields
    • 6. Endoscopy and Its Automorphisms
    • 7. A Conjectural Formula for Endoscopic Transfer
    • 8. Descent to Levi Subgroups
    • 9. Relevance Conditions for Langlands Parameters
    • 10. Endoscopy for Inner Forms of $GL_n$
    • 11. Local Langlands Correspondence for Inner Forms of $GL_n$
    • 12. $L$-packets for Inner Forms of $SL_n$
    • 13. $L$-packets for Inner Forms of $SL_n$ over Archimedean Fields
    • 14. Multiplicity Formula for $SL_n$
    • 15. Multiplicity Formula for Inner Forms of $SL_n$
    • 16. Lemmas for Trace Formula
    • 17. Trace Formula
    • A. Transfer Factors
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2152011; 97 pp
MSC: Primary 22; Secondary 11;

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 \(SL_n\).

  • Chapters
  • 1. Introduction
  • 2. Restriction of Representations
  • 3. Whittaker Normalization over Local Fields
  • 4. Restriction of Cusp Forms
  • 5. Whittaker Normalization over Global Fields
  • 6. Endoscopy and Its Automorphisms
  • 7. A Conjectural Formula for Endoscopic Transfer
  • 8. Descent to Levi Subgroups
  • 9. Relevance Conditions for Langlands Parameters
  • 10. Endoscopy for Inner Forms of $GL_n$
  • 11. Local Langlands Correspondence for Inner Forms of $GL_n$
  • 12. $L$-packets for Inner Forms of $SL_n$
  • 13. $L$-packets for Inner Forms of $SL_n$ over Archimedean Fields
  • 14. Multiplicity Formula for $SL_n$
  • 15. Multiplicity Formula for Inner Forms of $SL_n$
  • 16. Lemmas for Trace Formula
  • 17. Trace Formula
  • A. Transfer Factors
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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