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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

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

Citations:

Zbl 0644.00001