Flicker, Yuval Z. Regular trace formula and base change for \(GL(n)\). (English) Zbl 0691.10018 Ann. Inst. Fourier 40, No. 1, 1-30 (1990). The “regular” trace formula, for a test function with a local component which is Iwahori-biinvariant and sufficiently regular with respect to the other components, is developed in the context of a reductive group. It is used to give a simple proof of the theory of base-change for cuspidal automorphic representations of \(GL(n)\) which have a supercuspidal component. A purely local proof is given to transfer orbital integrals of sufficiently many spherical functions, by relating them to regular Iwahori functions. Transfer of orbital integrals of smooth functions is not used in the proof. Instead it is obtained as a corollary to the local lifting. Reviewer: Y.Z.Flicker Cited in 4 Documents MSC: 11F70 Representation-theoretic methods; automorphic representations over local and global fields 11F72 Spectral theory; trace formulas (e.g., that of Selberg) 11F85 \(p\)-adic theory, local fields 11R56 Adèle rings and groups 22E50 Representations of Lie and linear algebraic groups over local fields 22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings Keywords:Hecke algebra; Satake transform; matching solid companions; admissible representations; base-change lifting; test function; cuspidal automorphic representations; regular Iwahori functions PDFBibTeX XMLCite \textit{Y. Z. Flicker}, Ann. Inst. Fourier 40, No. 1, 1--30 (1990; Zbl 0691.10018) Full Text: DOI Numdam EuDML References: [1] [AC] , , Simple Algebras, Base Change and the Advanced Theory of the Trace Formula, Annales of Math. Study, 120 (1989). · Zbl 0682.10022 [2] [BDK] , , , Trace Paley-Wiener theorem, J. 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