3 Paths in type An � 1
نویسنده
چکیده
Littelmann has given a combinatorial model for the characters of representations of semisimple Lie algebras, in terms of certain paths traced in the space of (rational) weights. From it, a description of the decomposition of tensor products can be derived that generalises the Littlewood-Richardson rule (the latter is valid in type A n only). We present a new combinatorial construction that expresses in a bijective manner the symmetry of the tensor product in this path model. In type A n , where there is a correspondence between paths and skew tableaux, this construction is equivalent to Schh utzenberger's jeu de taquin; in the general case the construction retains its most crucial properties of symmetry and connuence.
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