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Littelmann's path crystal and combinatorics of certain sl_{l+1}^ modules of level zero

Jacob Greenstein
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Abstract

We construct a subcrystal of the Littelmann's path crystal whose formal character coincides with that of a certain simple integrable module of level zero over the untwisted affine Lie algebra associated to sl_n. We also establish an analogue of the Littlewood-Richardson rule for the tensor product of that crystal with a highest weight crystal.

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Jacob Greenstein. 2002-09-04. Littelmann's path crystal and combinatorics of certain sl_{l+1}^ modules of level zero. https://doi.org/10.1016/s0021-8693(03)00304-1

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