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Lie groupoids, the Satake compactification and the tempered dual, II: The Harish-Chandra principle (2511.22635v1)
Published 27 Nov 2025 in math.RT and math.OA
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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