# Compactification of semi-simple Lie groups.

@article{Albin2019CompactificationOS, title={Compactification of semi-simple Lie groups.}, author={Pierre b. Albin and Panagiotis Dimakis and Richard B. Melrose and David A. Vogan}, journal={arXiv: Differential Geometry}, year={2019} }

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…

## References

SHOWING 1-10 OF 23 REFERENCES

Resolution of smooth group actions

- Mathematics
- 2010

A refined form of the `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds…

An Introduction to Harmonic Analysis on Semisimple Lie Groups

- Mathematics
- 1989

Preface 1. Introduction 2. Compact groups: the work of Weyl 3. Unitary representations of locally compact groups 4. Parabolic induction, principal series representations, and their characters 5.…

Analytic continuation of the resolvent of the Laplacian on symmetric spaces of noncompact type

- Mathematics
- 2003

Spherical Varieties an Introduction

- Mathematics
- 1989

When one studies complex algebraic homogeneous spaces it is natural to begin with the ones which are complete (i.e. compact) varieties. They are the “generalized flag manifolds”. Their occurence in…

Generalized blow-up of corners and fiber products

- Mathematics
- 2011

Radial blow-up, including inhomogeneous versions, of boundary faces of a manifold (always with corners) is an important tool for resolving singularities, degeneracies and competing notions of…

Integral operators on the Oshima compactification of a Riemannian symmetric space of non-compact type. Regularized traces and characters

- Mathematics
- 2011

Consider a Riemannian symmetric space $X= G/K$ of non-compact type, where $G$ denotes a connected, real, semi-simple Lie group with finite center, and $K$ a maximal compact subgroup of $G$. Let…

Analytic continuation of the resolvent of the Laplacian on SL(3)/ SO(3)

- Mathematics
- 2002

In this paper we continue our program of extending the methods of geometric scattering theory to encompass the analysis of the Laplacian on symmetric spaces of rank greater than one and their…

On the wonderful compactification

- Mathematics
- 2008

These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a…

K‐theory of regular compactification bundles

- MathematicsMathematische Nachrichten
- 2022

Let G be a split connected reductive algebraic group. Let E⟶B$\mathcal {E}\longrightarrow \mathcal {B}$ be a G×G$G\times G$ ‐torsor over a smooth base scheme B$\mathcal {B}$ and X be a regular…