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arXiv · 2511.22635

Lie groupoids, the Satake compactification and the tempered dual, II: The Harish-Chandra principle

Jacob Bradd·Nigel Higson·Robert Yuncken
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Abstract

We give a geometric account of Harish-Chandra's principle that a tempered irreducible representation of a real reductive group is either square-integrable modulo center, or embeddable in a representation that is parabolically induced from such a representation. Our approach uses the Satake compactification, an associated groupoid that was constructed in the first paper of this series, and its $C^*$-algebra.

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Jacob Bradd, Nigel Higson, Robert Yuncken. 2025-11-27. Lie groupoids, the Satake compactification and the tempered dual, II: The Harish-Chandra principle. https://arxiv.org/abs/2511.22635

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