Flicker, Yuval Z. Relative trace formula and simple algebras. (English) Zbl 0623.22016 Proc. Am. Math. Soc. 99, 421-426 (1987). Let E/F be a quadratic extension of global fields, G a reductive F-group. A cuspidal \(G({\mathbb{A}}_ E)\)-module is said to be distinguished if it has an integrable function whose integral over \(G(F)/G({\mathbb{A}}_ F)\) is nonzero. Let G be the multiplicative group of a central simple algebra divided by centre and G’ be GL(n) divided by centre. Suppose the \(G({\mathbb{A}}_ E)\)-module \(\pi\) corresponds by Deligne-Kazhdan correspondence to the \(G'({\mathbb{A}}_ E)\)-module \(\pi\) ’, by a good choice of the function f defining the kernel of the right regular representation the author obtains a simple relative trace formula which he uses to prove under certain ramification assumptions that \(\pi\) is distinguished if and only if \(\pi\) ’ is distinguished. Reviewer: K.Lai Cited in 1 ReviewCited in 4 Documents MSC: 22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings 11R39 Langlands-Weil conjectures, nonabelian class field theory 11F70 Representation-theoretic methods; automorphic representations over local and global fields Keywords:rings of adeles; distinguished cuspidal module; quadratic extension; reductive F-group; central simple algebra; Deligne-Kazhdan correspondence; regular representation; relative trace formula PDFBibTeX XMLCite \textit{Y. Z. Flicker}, Proc. Am. Math. Soc. 99, 421--426 (1987; Zbl 0623.22016) Full Text: DOI References: [1] Tetsuya Asai, On certain Dirichlet series associated with Hilbert modular forms and Rankin’s method, Math. Ann. 226 (1977), no. 1, 81 – 94. · Zbl 0326.10024 · doi:10.1007/BF01391220 [2] Y. Flicker, Representations of simple algebras, mimeographed notes, based on a course at Harvard University, fall 1985. [3] -, Twisted tensors and Euler products, preprint, Harvard Univ., 1985. [4] H. Jacquet and K. F. Lai, A relative trace formula, Compositio Math. 54 (1985), no. 2, 243 – 310. · Zbl 0587.12006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.