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A splitting criterion for the Bruhat orderings on Coxeter groups. (English) Zbl 0631.20030
From the introduction: The aim of this short note is to prove a useful property of the Bruhat ordering on a Coxeter group (W,S). Let \(J\subseteq S\) be a subset and \(W^ J\) be the set of minimal representatives of the left cosets of the subgroup \(W_ J\) generated by J. The Bruhat ordering on W induces one on \(W^ J\) and \(W_ J\) as well. In this note we prove that one can recover the Bruhat order on W from those on \(W_ J\) and \(W^ J\) using some functions from \(W_ J\) to \(W_ J\). We show that these functions are completely determined by the image of identity e.
Reviewer: E.W.Ellers

MSC:
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
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[1] DOI: 10.1007/BF01390109 · Zbl 0333.20041 · doi:10.1007/BF01390109
[2] DOI: 10.1007/BF02842481 · doi:10.1007/BF02842481
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