Compactification of semi-simple Lie groups
Differential Geometry
2019-10-08 v1 Group Theory
Abstract
We discuss the `hd-compactification' of a semi-simple Lie group to a manifold with corners; it is the real analog of the wonderful compactification of deConcini and Procesi. There is a 1-1 correspondence between the boundary faces of the compactification and conjugacy classes of parabolic subgroups with the boundary face fibering over two copies of the corresponding flag variety with fiber modeled on the (compactification of the) reductive part. On the hd-compactification Harish-Chandra's Schwartz space is identified with a space of conormal functions of rapid-logarithmic decay relative to square-integrable functions.
Cite
@article{arxiv.1910.02811,
title = {Compactification of semi-simple Lie groups},
author = {Pierre Albin and Panagiotis Dimakis and Richard Melrose and David Vogan},
journal= {arXiv preprint arXiv:1910.02811},
year = {2019}
}