Arthur, James Characters, harmonic analysis, and an \(L^ 2\)-Lefschetz formula. (English) Zbl 0671.22007 The mathematical heritage of Hermann Weyl, Proc. Symp., Durham/NC 1987, Proc. Symp. Pure Math. 48, 167-179 (1988). [For the entire collection see Zbl 0644.00001.] In this lecture a Lefschetz formula for the action of Hecke operators on the \(L^ 2\)-cohomology of G(\({\mathbb{Q}})\setminus G({\mathbb{A}})/K\) is announced (G a reductive group over \({\mathbb{Q}}\), K compact subgroup). The discussion of the formula is preceded by a short survey of Weyl’s classification of representations of compact Lie groups and Harish- Chandra’s theory of the discrete series. For the proof of the Lefschetz formula see [the author, Invent. Math. 97, No.2, 257-290 (1989)]. Reviewer: J.G.M.Mars Cited in 1 Document MSC: 22E46 Semisimple Lie groups and their representations 11F70 Representation-theoretic methods; automorphic representations over local and global fields 11F27 Theta series; Weil representation; theta correspondences 57T10 Homology and cohomology of Lie groups Keywords:Lefschetz formula; action of Hecke operators; \(L^ 2\)-cohomology; reductive group; representations of compact Lie groups; discrete series Citations:Zbl 0644.00001 PDFBibTeX XML