On inversion sets and the weak order in Coxeter groups
Copyright policy )On inversion sets and the weak order in Coxeter groups
In this article, we investigate the existence of joins in the weak order of an infinite Coxeter group W. We give a geometric characterization of the existence of a join for a subset X in W in terms of the inversion sets of its elements and their position relative to the imaginary cone. Finally, we discuss inversion sets of infinite reduced words and the notions of biconvex and biclosed sets of positive roots.
22 pages; 10 figures; v2 some references were added; v2: final version, to appear in European Journal of Combinatorics
- Université du Québec à Montréal Canada
- Université du Québec à Montréal Canada
- Hebrew University of Jerusalem Israel
- University of Quebec Canada
biclosed sets, inversion sets, 20F55, Secondary 06B23, 05E15, biconvex sets, Coxeter groups, Group Theory (math.GR), biconvex sets of positive roots, inversion sets of infinite reduced words, Cayley graphs, Graphs and abstract algebra (groups, rings, fields, etc.), Reflection and Coxeter groups (group-theoretic aspects), weak order, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Root systems, limit roots, biclosed sets of positive roots, Mathematics - Group Theory
biclosed sets, inversion sets, 20F55, Secondary 06B23, 05E15, biconvex sets, Coxeter groups, Group Theory (math.GR), biconvex sets of positive roots, inversion sets of infinite reduced words, Cayley graphs, Graphs and abstract algebra (groups, rings, fields, etc.), Reflection and Coxeter groups (group-theoretic aspects), weak order, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Root systems, limit roots, biclosed sets of positive roots, Mathematics - Group Theory
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