Finite Crystals and Paths
量子代数
2007-05-23 v2 高能物理 - 理论
数学物理
math.MP
摘要
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.
引用
@article{arxiv.math/9901082,
title = {Finite Crystals and Paths},
author = {Goro Hatayama and Yoshiyuki Koga and Atsuo Kuniba and Masato Okado and Taichiro Takagi},
journal= {arXiv preprint arXiv:math/9901082},
year = {2007}
}
备注
15 pages, LaTeX2e, submitted to the proceedings of the RIMS98 program "Combinatorial Methods in Representation Theory"