Paths, crystals and fermionic formulae
Paths, crystals and fermionic formulae
复制标题
路径、晶体和费米子公式
DOI：
10.1007/978-1-4612-0087-1_9
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发表时间：
2001
影响因子：
2.5
通讯作者：
Z. Tsuboi
中科院分区：
文献类型：
--
作者：
G. Hatayama;A. Kuniba;M. Okado;T. Takagi;Z. Tsuboi
引入了一个与任意量子仿射代数Uq（XN（r））相关联的费米子公式.在可解格点模型中角转移矩阵和Bethe矩阵的相互作用的指导下，我们研究了与表示论相关的几个方面，其中最重要的是晶体基理论。其中包括有限和半无限路径上的一维和，旋子特征公式，真空弦函数的Lepowsky-Primc型代数公式，双对数恒等式，Q-系统及其利用各种经典子代数特征的解等等。结果扩展了[HKOTY 1]，包括扭曲的情况和由非完美晶体组成的非均匀路径的更多细节。作为一个最有趣的例子，某些非齐次的一维和在理论上产生了与嵌入G2（1）<B（1）<$D41相关的可积G2（1）-模的分支函数。
We introduce a fermionic formula associated with any quantum affine algebra U q (X N (r) . Guided by the interplay between corner transfer matrix and the Bethe ansatz in solvable lattice models, we study several aspects related to representation theory, most crucially, the crystal basis theory. They include one-dimensional sums over both finite and semi-infinite paths, spinon character formulae, Lepowsky—Primc type conjectural formula for vacuum string functions, dilogarithm identities, Q-systems and their solution by characters of various classical subalgebras and so forth. The results expand [HKOTY1] including the twisted cases and more details on inhomogeneous paths consisting of non-perfect crystals. As a most intriguing example, certain inhomogeneous one-dimensional sums conjecturally give rise to branching functions of an integrable G 2 (1) -module related to the embedding G 2 (1) ↪ B 3 (1) ↪ D 4 1 .