Memoirs of the American Mathematical Society 2011; 97 pp; softcover Volume: 215 ISBN10: 0821853643 ISBN13: 9780821853641 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 wellknown paper of Labesse and Langlands (Lindistinguishability for SL\((2)\). Canad. J. Math. 31 (1979), no. 4, 726785). 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, 305379, 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
