On minimal lengths of expressions of Coxeter group elements as products of reflections

Author:

Dyer Matthew

Abstract

It is shown that the absolute length l ( w ) l’(w) of a Coxeter group element w w (i.e. the minimal length of an expression of w w as a product of reflections) is equal to the minimal number of simple reflections that must be deleted from a fixed reduced expression of w w so that the resulting product is equal to e e , the identity element. Also, l ( w ) l’(w) is the minimal length of a path in the (directed) Bruhat graph from the identity element e e to w w , and l ( w ) l’(w) is determined by the polynomial R e , w R_{e,w} of Kazhdan and Lusztig.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference13 articles.

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2. N. Bourbaki, Groupes ét algebres de Lie, Ch. 4–6, Hermann, Paris, 1964.

3. A combinatorial formula for Kazhdan-Lusztig polynomials;Brenti, Francesco;Invent. Math.,1994

4. Conjugacy classes in the Weyl group;Carter, R. W.;Compositio Math.,1972

5. On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells;Deodhar, Vinay V.;Invent. Math.,1985

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