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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)].

##### 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
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