Titlebook: An Introduction to Automorphic Representations; With a view toward t Jayce R. Getz,Heekyoung Hahn Textbook 2024 Springer Nature Switzerland

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,Reformvorschl?ge und deren Umsetzbarkeit,In this chapter, we describe the classification of unramified representations of reductive groups over non-Archimedean local fields. Along the way, we discuss the Satake isomorphism and the Langlands dual group.

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Markus H. Dahm,Marielena WinterThe cuspidal spectrum of . decomposes discretely into a Hilbert space direct sum with finite multiplicities. We give a proof of this fact in this chapter. We also prove that cuspidal automorphic forms are rapidly decreasing in the number field case and are compactly supported in the function field case.

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https://doi.org/10.1007/978-3-658-17683-9In this chapter we discuss the notion of a distinguished representation in local and global contexts. The global notion is defined in terms of period integrals and hence isolates a crucial link between automorphic representation theory and the geometry of locally symmetric spaces.

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Einführung in die Gesamt-StudieWe discuss how automorphic representation theory controls the cohomology of arithmetic locally symmetric spaces.

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