Automorphic forms on \(\text{SO}(4)\). (English) Zbl 1061.11022

This paper is an announcement of the results on automorphic forms on \(\text{SO}(4)\) from the preprint [Y. Flicker, Lifting automorphic forms of \(\text{PGSp}(2)\) and \(\text{SO}(4)\) to \(\text{PGL}(4)\) (2001)].
The study of the stabilization of the twisted trace formula in [loc. cit.] leads to a theory of lifting of automorphic representations of \(\text{PGSp}(2)\) and \(\text{SO}(4)\) to \(\text{ PGL}(4)\). The announcement of the results for \(\text{PGSp}(2)\) is published in [Y. Flicker, Automorphic forms on \(\text{PGSp}(2)\), Electron. Res. Announc. Am. Math. Soc. 10, 39–50 (2004; Zbl 1062.11027)].
The paper under review states the results on endoscopic lifting from \(\text{SO}(4)\) to \(\text{PGL}(4)\). The first result is the statement that the functorial product of two automorphic representations \(\pi_1\) and \(\pi_2\) of \(\text{GL}(2, \mathbb{A})\) whose central characters \(\omega_1\), \(\omega_2\) satisfy \(\omega_1 \omega_2=1\) exists as an automorphic representation of \(\text{PGL}(4, \mathbb{A})\). The second statement is a rigidity theorem for the automorphic representations of \(\text{SO}(4)\).


11F70 Representation-theoretic methods; automorphic representations over local and global fields
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
22E46 Semisimple Lie groups and their representations
11F55 Other groups and their modular and automorphic forms (several variables)


Zbl 1062.11027
Full Text: DOI Euclid


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