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The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a -ideal of the special -ring of symmetric group class functions.
Nous définissons et entamons l’étude d’analogues infinitésimaux des quotients principaux
(algèbres de Temperley-Lieb, Hecke, Birman-Wenzl-Murakami) de l’algèbre de groupe du
groupe d’Artin . Ce sont des algèbres de Hopf qui correspondent à des groupes
réductifs, et permettent de donner un cadre général aux représentations dérivées des
représentations classiques de . Nous décomposons complètement l’algèbre de
Temperley-Lieb infinitésimale, et en déduisons plusieurs résultats d’irréductibilité.
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