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CAP-Localization

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1968)

Abstract

In this chapter, we will express the π-isotypic Lefschetz numbers of Hecke operators acting on the cohomology of symmetric spaces SK(G) attached to reductive groups G in terms of so-called elliptic traces Tell, provided the underlying representation π is not a cuspidal representation associated with a parabolic subgroup (CAP representation) of G(A). In the following two chapters we derive from these formulas all the essential information required.

Keywords

  • Conjugacy Class
  • Parabolic Subgroup
  • Maximal Compact Subgroup
  • Levi Subgroup
  • Automorphic Representation

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Correspondence to Rainer Weissauer .

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© 2009 Springer-Verlag Berlin Heidelberg

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Weissauer, R. (2009). CAP-Localization. In: Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds. Lecture Notes in Mathematics(), vol 1968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89306-6_2

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