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On the symmetric square: Total global comparison. (English) Zbl 0815.11030

This paper is the last in a series which the author has devoted to studying the so-called symmetric square lift of automorphic forms from SL(2) to PGL(3). The proof is based on the trace formula which in this case is very delicate and which has been spread out over the series. In this paper he treats the global comparison between the trace formulae for the two groups.
The Main Theorem which he proves is a Strong Multiplicity One Theorem for SL(2), namely that if two cuspidal representations are equal almost everywhere then they belong to the same \(L\)-packet, and that if the representations are equal everywhere then they are, as automorphic representations, identical. He also shows that the lift to PGL(3) is defined and characterizes its image. The proof is a continuation of the other papers in the series. There are also, in this paper, some corrections to other papers in the series.

MSC:

11F72 Spectral theory; trace formulas (e.g., that of Selberg)
22E50 Representations of Lie and linear algebraic groups over local fields
11F70 Representation-theoretic methods; automorphic representations over local and global fields
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