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

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

2002-06-25

arxiv.org/abs/math/0206263v2

J. Algebra, 269 (2003), no. 1, 347-372

Mathematics

Quantum Algebra

25 pages, AMSLaTeX; to appear in the "Journal of Algebra"

Scientific paper

10.1016/S0021-8693(03)00304-1

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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