The Kirillov-Reshetikhin conjecture and solutions of T-systems
The Kirillov-Reshetikhin conjecture and solutions of T-systems
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DOI：
10.1515/crelle.2006.052
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发表时间：
2006-07-01
影响因子：
1.5
通讯作者：
Hernandez, David
中科院分区：
文献类型：
--
作者：
Hernandez, David
我们证明了所有无扭量子仿射代数的Kirillov-Reshetikhin猜想：我们证明了Kirillov-Reshetikhin模的特征标解Q-系统，并给出了它们张量积的特征标的一个显式公式.在证明中，我们表明Kirillov-Reshetikhin模是特殊的单项式的意义下，他们的q-字符解决的T-系统（功能关系出现在可解格模型的研究）。此外，我们证明了T-系统可以写成正合序列的形式。对于简单的情形，Nakajima在[31]，[32]中用几何论证证明了这些结果（[31]的主要结果），而这些结果在一般情况下是不可用的。我们使用的证明是不同的和纯代数的，因此可以统一地扩展到非简单的情况。
We prove the Kirillov-Reshetikhin conjecture for all untwisted quantum affine algebras: we prove that the characters of Kirillov-Reshetikhin modules solve the Q-system and we give an explicit formula for the character of their tensor products. In the proof we show that Kirillov-Reshetikhin modules are special in the sense of monomials and that their q-characters solve the T-system (functional relations appearing in the study of solvable lattice models). Moreover we prove that the T-system can be written in the form of an exact sequence. For simply-laced cases, these results were proved by Nakajima in [31], [32] with geometric arguments (main result of [31]) which are not available in general. The proof we use is different and purely algebraic, and so can be extended uniformly to non simply-laced cases.