Finite Crystals and Paths
Goro Hatayama, Yoshiyuki Koga, Atsuo Kuniba, Masato Okado, Taichiro Takagi
Abstract
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 Cn(1) and An-1(1), in which the direct sum becomes a tensor product as suggested from the Bethe Ansatz.
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