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arXiv · 1507.01521

Tower of fully commutative elements of type $\tilde A$ and applications

Sadek Al Harbat
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Abstract

Let $W^c(\tilde A_{n})$ be the set of fully commutative elements in the affine Coxeter group $W(\tilde A_{n})$ of type $\tilde{A}$. We classify the elements of $W^c(\tilde A_{n})$ 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 $W^c(\tilde A_{n-1})$ into $W^c(\tilde A_{n})$ and examine their properties. We then consider the tower of affine Temperley-Lieb algebras of type $\tilde{A }$ and use the injections above to prove the injectivity of this tower.

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Sadek Al Harbat. 2015-07-06. Tower of fully commutative elements of type $\tilde A$ and applications. https://arxiv.org/abs/1507.01521

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