Finite Crystals and Paths
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We consider a category of finite crystals of a quantum affine algebra whose objects are not necessarily perfect, and set of paths, semi-infinite tensor product of an object of this category with a certain boundary condition. It is shown that the set of paths is isomorphic to a direct sum of infinitely many, in general, crystals of integrable highest weight modules. We present examples from C_n^{(1)} and A_{n-1}^{(1)}, in which the direct sum becomes a tensor product as suggested from the Bethe Ansatz.
15 pages, LaTeX2e, submitted to the proceedings of the RIMS98 program "Combinatorial Methods in Representation Theory"
15 pages, LaTeX2e, submitted to the proceedings of the RIMS98 program "Combinatorial Methods in Representation Theory"