Automorphic forms on \(\text{SO}(4)\).
This paper is an announcement of the results on automorphic forms on \(\text{SO}(4)\) from the preprint [\textit{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 [\textit{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 \(\text{SO}(4)\).
scientific article; zbMATH DE number 2138347
scientific article