{
"id": "1803.04945",
"version": "v1",
"published": "2018-03-13T17:24:01.000Z",
"updated": "2018-03-13T17:24:01.000Z",
"title": "On fully commutative elements of type $\\tilde B$ and $\\tilde D$",
"authors": [
"Sadek AL Harbat"
],
"categories": [
"math.GR"
],
"abstract": "We define a tower of injections of $\\tilde{B}$-type (resp. $\\tilde{D}$-type) Coxeter groups $W(\\tilde B_{n})$ (resp. $W(\\tilde D_{n})$) for $n\\geq 3$. Let $W^c(\\tilde B_{n})$ (resp. $W^c(\\tilde D_{n})$) be the set of fully commutative elements in $W(\\tilde B_{n})$ (resp. $W(\\tilde D_{n})$), we classify the elements of this set by giving a normal form for them. We define a $\\tilde{B}$-type tower of Hecke algebras and we use the faithfulness at the Coxeter level to show that this last tower is a tower of injections. We use this normal form to define two injections from $W^c(\\tilde B_{n-1})$ into $W^c(\\tilde B_{n})$. We then define the tower of affine Temperley-Lieb algebras of type $\\tilde{B }$ and use the injections above to prove the faithfulness of this tower. We follow the same track for $\\tilde{D}$-type objects",
"revisions": [
{
"version": "v1",
"updated": "2018-03-13T17:24:01.000Z"
}
],
"analyses": {
"subjects": [
"20F36",
"20F55"
],
"keywords": [
"fully commutative elements",
"injections",
"normal form",
"affine temperley-lieb algebras",
"type objects"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}