Lie groupoids, the Satake compactification and the tempered dual, II: The Harish-Chandra principle
Representation Theory
2025-12-01 v1 Operator Algebras
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 -algebra.
Keywords
Cite
@article{arxiv.2511.22635,
title = {Lie groupoids, the Satake compactification and the tempered dual, II: The Harish-Chandra principle},
author = {Jacob Bradd and Nigel Higson and Robert Yuncken},
journal= {arXiv preprint arXiv:2511.22635},
year = {2025}
}