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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
##### Keywords:
Bruhat ordering; Coxeter group
Full Text:
##### References:
 [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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