Tower of fully commutative elements of type A and applications

2015/07/06 by Sadek Al Harbat, Harbat, Sadek Al
Mathematics · #20F36 #20F55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1507.01521

openalex publication_date 2015/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let W^c( A_n) be the set of fully commutative elements in the affine Coxeter group W( A_n) of type A. We classify the elements of W^c( A_n) and give a normal form for its elements. We give a first application of this normal form to fully commutative affine braids. We then use this normal form to define two injections from W^c( A_n-1) into W^c( A_n) and examine their properties. We then consider the tower of affine Temperley-Lieb algebras of type A and use the injections above to prove the injectivity of this tower.

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