Freely Braided Elements in Coxeter Groups
نویسندگان
چکیده
We introduce a notion of " freely braided element " for simply laced Cox-eter groups. We show that an arbitrary group element w has at most 2 N (w) com-mutation classes of reduced expressions, where N(w) is a certain statistic defined in terms of the positive roots made negative by w. This bound is achieved if w is freely braided. In the type A setting, we show that the bound is achieved only for freely braided w.
منابع مشابه
Braided Elements in Coxeter Groups , Ii
We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work. A known upper bound for the number of commutation classes of reduced expressions for an element of a simply laced Coxeter group is shown to be achieved only when the element is freely braided; this establishes the converse direction of a previous result. It is also shown that...
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