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VOL. 28 | 2000 Finite Crystals and Paths
Goro Hatayama, Yoshiyuki Koga, Atsuo Kuniba, Masato Okado, Taichiro Takagi

Editor(s) Kazuhiko Koike, Masaki Kashiwara, Soichi Okada, Itaru Terada, Hiro-Fumi Yamada


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.


Published: 1 January 2000
First available in Project Euclid: 20 August 2018

zbMATH: 1008.17009
MathSciNet: MR1864478

Digital Object Identifier: 10.2969/aspm/02810113

Rights: Copyright © 2000 Mathematical Society of Japan


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