Deodhar, Vinay V. A splitting criterion for the Bruhat orderings on Coxeter groups. (English) Zbl 0631.20030 Commun. Algebra 15, 1889-1894 (1987). 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 Cited in 8 Documents MSC: 20G20 Linear algebraic groups over the reals, the complexes, the quaternions Keywords:Bruhat ordering; Coxeter group PDF BibTeX XML Cite \textit{V. V. Deodhar}, Commun. Algebra 15, 1889--1894 (1987; Zbl 0631.20030) Full Text: DOI References: [1] DOI: 10.1007/BF01390109 · Zbl 0333.20041 · doi:10.1007/BF01390109 [2] DOI: 10.1007/BF02842481 · doi:10.1007/BF02842481 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.