Finite Crystals and Paths

Abstract

We consider a category of finite crystals of a quantum affine algebra whose objects are not necessarily perfect, and set of paths, semiinfinite 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.