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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

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 $$SL_n$$.

• 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