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On minimal lengths of expressions of Coxeter group elements as products of reflections
Author(s):
Matthew
J.
Dyer
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2591-2595.
MSC (2000):
Primary 20F55, 22E47, 06A07
Posted:
February 9, 2001
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Abstract:
It is shown that the absolute length  of a Coxeter group element  (i.e. the minimal length of an expression of  as a product of reflections) is equal to the minimal number of simple reflections that must be deleted from a fixed reduced expression of  so that the resulting product is equal to  , the identity element. Also,  is the minimal length of a path in the (directed) Bruhat graph from the identity element  to  , and  is determined by the polynomial  of Kazhdan and Lusztig.
References:
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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:
10.1090/S0002-9939-01-05876-2
PII:
S 0002-9939(01)05876-2
Received by editor(s):
August 23, 1999
Received by editor(s) in revised form:
January 27, 2000
Posted:
February 9, 2001
Communicated by:
John R. Stembridge
Copyright of article:
Copyright
2001,
American Mathematical Society
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