Normalisateurs et groupes d’Artin-Tits de type sphérique
نویسنده
چکیده
Let (AS , S) be an Artin-Tits and X a subset of S ; denote by AX the subgroup of AS generated by X. When AS is of spherical type, we prove that the normalizer and the commensurator of AX in AS are equal and are the product of AX by the quasi-centralizer of AX in AS . Looking to the associated monoids A + S and A + X , we describe the quasi-centralizer of A+X in A + S thanks to results in Coxeter groups. These two results generalize earlier results of Paris ([11]). Finaly, we compare, in the spherical case, the normalizer of a parabolic subgroup in the Artin-Tits group and in the Coxeter group. 2000 Mathematics Subject Classification: 20F36.
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