On the fully commutative elements of Coxeter groups
John R. Stembridge
University of Michigan Department of Mathematics 48109-1109 Ann Arbor Michigan 48109-1109 Ann Arbor Michigan
DOI: 10.1007/BF00193185
Abstract
Let W be a Coxeter group. We define an element w ϵW to be fully commutative if any reduced expression for w can be obtained from any other by means of braid relations that only involve commuting generators. We give several combinatorial characterizations of this property, classify the Coxeter groups with finitely many fully commutative elements, and classify the parabolic quotients whose members are all fully commutative. As applications of the latter, we classify all parabolic quotients with the property that (1) the Bruhat ordering is a lattice, (2) the Bruhat ordering is a distributive lattice, (3) the weak ordering is a distributive lattice, and (4) the weak ordering and Bruhat ordering coincide.
Pages: 353–385
Keywords: Coxeter group; reduced word; heap; weak order; Bruhat order
Full Text: PDF
References
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