The Alcove Path Model and Tableaux
نویسندگان
چکیده
The second author and Postnikov have recently constructed a simple combinatorial model for the characters of the irreducible representations of a complex semisimple Lie group, that is referred to as the alcove path model. In this paper we relate the alcove path model to the the semistandard Young tableaux in type A and the KashiwaraNakashima tableaux in type C. More explicitly, we construct bijections between the objects in the alcove path model (certain saturated chains in the Bruhat order on the corresponding Weyl group) and the corresponding tableaux. We show that this bijection preserves the corresponding crystal structures, and we give applications to Demazure characters and basis constructions.
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