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Finite Crystals and Paths

Goro Hatayama·Yoshiyuki Koga·Atsuo Kuniba·Masato Okado·Taichiro Takagi
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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 C_n^{(1)} and A_{n-1}^{(1)}, in which the direct sum becomes a tensor product as suggested from the Bethe Ansatz.

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Goro Hatayama, Yoshiyuki Koga, Atsuo Kuniba, Masato Okado, Taichiro Takagi. 1999-02-10. Finite Crystals and Paths. https://arxiv.org/abs/math/9901082

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