On $L$-Packets for Inner Forms of $SL_

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 $SL_n$.