On rigidity of abstract root systems of Coxeter systems

2010/11/10 by Matthew Dyer, Dyer, Matthew · 2 citations
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1011.2270

Abstract

We introduce and study a combinatorially defined notion of root basis of a (real) root system of a possibly infinite Coxeter group. Known results on conjugacy up to sign of root bases of certain irreducible finite rank real root systems are extended to abstract root bases, to a larger class of real root systems, and, with a short list of (genuine) exceptions, to infinite rank irreducible Coxeter systems.

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• Groupoids, root systems and weak order II
• Oriented Matroid Structures From Realized Root Systems

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