NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS

Authors : Dana C Ernst

Pages : 191-218

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Publication Date : 2010-12-01

Article Type : Research Paper

Abstract :Let insert ignore into journalissuearticles values(W, S); be a Coxeter system and suppose that w ∈ W is fully commutative insert ignore into journalissuearticles values(in the sense of Stembridge); and has a reduced expression beginning insert ignore into journalissuearticles values(respectively, ending); with s ∈ S. If there exists t ∈ S such that s and t do not commute and tw insert ignore into journalissuearticles values(respectively, wt); is no longer fully commutative, we say that w is left insert ignore into journalissuearticles values(respectively, right); weak star reducible by s with respect to t. We say that a fully commutative element is non-cancellable if it is irreducible under weak star reductions. In this paper, we classify the noncancellable elements in Coxeter groups of types B and affine C. In a sequel to this paper, the classification of the non-cancellable elements play a pivotal role in inductive arguments used to prove the faithfulness of a diagrammatic representation of a generalized Temperley–Lieb algebra of type affine C.
Keywords : Coxeter groups, non cancellable, star operations, heaps