Polar decomposition for p-adic symmetric spaces
Group Theory
2007-05-23 v1 Number Theory
Abstract
Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution s of G. We prove a polar decomposition G=KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of the groups of k-points of maximal (k,s)-split tori, one for each H-conjugacy class. This decomposition is analogous to the well-known polar decomposition G=KAH for a real symmetric space G/H.
Cite
@article{arxiv.math/0612305,
title = {Polar decomposition for p-adic symmetric spaces},
author = {Yves Benoist and Hee Oh},
journal= {arXiv preprint arXiv:math/0612305},
year = {2007}
}
Comments
16 pages