Rogawski, Jonathan D. Automorphic representations of unitary groups in three variables. (English) Zbl 0724.11031 Annals of Mathematics Studies, 123. Princeton, NJ: Princeton University Press. xii, 259 p. $ 60.00/hbk; $ 19.95/pbk (1990). In the first ten chapters of this book the stabilization of Arthur’s trace formula is effectuated for the quasi-split U(3) and the comparison of ordinary and twisted trace formula is made. This enables the author to derive the following results on admissible resp. automorphic representations. 1) Locally: The partition of the set of irreducible admissible representations of U(3) into L-packets. The correspondence between L-packets of the endoscopic group U(2)\(\times U(1)\) and L-packets of U(3). Local base change for U(3). 2) Globally: Multiplicity one. A decription of the set of discrete global L-packets for U(3). Base change. A description of the discrete spectrum. Also considered are: The correspondence between global L-packets for U(3) and an inner form of U(3). The local Langlands correspondence. The questions treated in this book are also treated by Y. Z. Flicker [J. Anal. Math. 50, 19-63 (1988; Zbl 0666.10019) and ibid. 52, 39-52 (1989; Zbl 0684.10027)]. Reviewer: J.G.M.Mars (Utrecht) Cited in 13 ReviewsCited in 99 Documents MSC: 11F70 Representation-theoretic methods; automorphic representations over local and global fields 22E50 Representations of Lie and linear algebraic groups over local fields 11F72 Spectral theory; trace formulas (e.g., that of Selberg) 11-02 Research exposition (monographs, survey articles) pertaining to number theory 22-02 Research exposition (monographs, survey articles) pertaining to topological groups Keywords:Arthur’s trace formula; quasi-split U(3); automorphic representations; admissible representations; L-packets; endoscopic group; Base change; discrete spectrum; local Langlands correspondence Citations:Zbl 0666.10019; Zbl 0684.10027 × Cite Format Result Cite Review PDF Full Text: DOI