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


Author: Matthew J. Dyer
Journal: Proc. Amer. Math. Soc. 129 (2001), 2591-2595
MSC (2000): Primary 20F55, 22E47, 06A07
DOI: https://doi.org/10.1090/S0002-9939-01-05876-2
Published electronically: February 9, 2001
MathSciNet review: 1838781
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Abstract:

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


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Additional Information

Matthew J. Dyer
Affiliation: Department of Mathematics, University of Notre Dame, Room 370 CCMB, Notre Dame, Indiana 46556-5683
Email: Dyer.1@nd.edu

DOI: https://doi.org/10.1090/S0002-9939-01-05876-2
Received by editor(s): August 23, 1999
Received by editor(s) in revised form: January 27, 2000
Published electronically: February 9, 2001
Communicated by: John R. Stembridge
Article copyright: © Copyright 2001 American Mathematical Society

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