超平面排列的量子可积模型
Quantum Integrable Model of an Arrangement of Hyperplanes
摘要：
本文的目的是给出一个与简单李代数相关联的Gaudin模型的Bethe代数（Hamilton算子）的尺规作图法。更准确地说，本文将量子可积模型赋给了一个加权的仿射超平面排列。我们表明（在一定的假设下），该模型的哈密顿代数是同构于相应的主函数的临界集上的函数代数。对于一个判别安排，我们表明（在一定的假设下），对称部分的代数哈密顿同构的贝特代数相应的高丁模型。预计这种对应关系通常成立（没有假设）。作为一个副产品的建设，我们表明，在一个Gaudin模型（与任意简单的李代数），贝特向量，对应于一个孤立的临界点的主功能，是非零的。
英文摘要：
The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted arrangement of affine hyperplanes. We show (under certain assumptions) that the algebra of Hamiltonians of the model is isomorphic to the algebra of functions on the critical set of the corresponding master function. For a discriminantal arrangement we show (under certain assumptions) that the symmetric part of the algebra of Hamiltonians is isomorphic to the Bethe algebra of the corresponding Gaudin model. It is expected that this correspondence holds in general (without the assumptions). As a byproduct of constructions we show that in a Gaudin model (associated to an arbitrary simple Lie algebra), the Bethe vector, corresponding to an isolated critical point of the master function, is nonzero.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
