arXiv:1507.01521 [math.GR]AbstractReferencesReviewsResources
Tower of fully commutative elements of type $\tilde A$ and applications
Published 2015-07-06Version 1
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.
Comments: 23 p. The normal form for affine fully commutative elements of type $\tilde A$ and for fully commutative affine braids was established in arXiv:1311.7089 "A classification of affine fully commutative elements". We have made some changes in the notations and we have added a new application to the injectivity of the tower of affine Temperley-Lieb algebras of type $tilde A$
Categories: math.GR
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