THE K ( n , I )-PROBLEM FOR HYPERPLANE COMPLEMENTS ASSOCIATED TO INFINITE REFLECTION GROUPS

@inproceedings{Charney2009THEK,
title={THE K ( n , I )-PROBLEM FOR HYPERPLANE COMPLEMENTS ASSOCIATED TO INFINITE REFLECTION GROUPS},
author={Ruth Charney and Michael W. Davis},
year={2009}
}

We begin by recalling some well-known facts. The natural action of the symmetric group Sn on jRn can be viewed as a group generated by reflections. The reflections in Sn are the orthogonal reflections across the hyperplanes H jj = {x E jRnlxj = x j }, 1 '.5, i < j '.5, n. The Sn-action extends to Cn (= jRn ®C) and the set of points with nontrivial isotropy group is U H jj ® C. Let M denote the quotient manifold,