r矩阵及其应用的进展(根据Maulik-Okounkov, Kang-Kashiwara-Kim-Oh，…)

IF 1 4区数学 Q1 MATHEMATICS

Asterisque Pub Date : 2017-04-20 DOI:10.24033/ast.1067

David Hernandez

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引用次数: 19

摘要

R-矩阵是杨-巴克斯特方程的解。在量子群论的起源，它们可以被解释为纠缠的算符。最近的进展是在不同的方向上独立取得的。Maulik Okounkov利用辛几何中的新工具，即稳定包络，给出了R矩阵的几何方法。Kang Kashiwara Kim Oh用R-矩阵证明了簇代数范畴化的一个猜想。最终，对从R-矩阵得到的转移矩阵的作用有了更好的理解，从而证明了关于相应量子可积系统的几个猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Avancées concernant les R-matrices et leurs applications (d’après Maulik-Okounkov, Kang-Kashiwara-Kim-Oh, ...)

R-matrices are the solutions of the Yang-Baxter equation. At the origin of the quantum group theory, they may be interpreted as intertwining operators. Recent advances have been made independently in different directions. Maulik-Okounkov have given a geometric approach to R-matrices with new tools in symplectic geometry, the stable envelopes. Kang-Kashiwara-Kim-Oh proved a conjecture on the categorification of cluster algebras by using R-matrices in a crucial way. Eventually, a better understanding of the action of transfer-matrices obtained from R-matrices led to the proof of several conjectures about the corresponding quantum integrable systems.

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来源期刊

Asterisque MATHEMATICS-

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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