论文标题
四面体方程和集群代数的溶液
Solution of tetrahedron equation and cluster algebras
论文作者
论文摘要
我们注意到Zamolodchikov四面体方程的Bazhanov-Sergeev解决方案与某些众所周知的群集代数表达之间。然后用四个突变序列鉴定四面体转化。作为新形式主义的应用，我们展示了如何用任意对称的牛顿多边形构建光谱曲线的可集成系统。最后，我们将这个可集成的系统嵌入了泊松组的双bruhat细胞中，展示了如何使用三角形分解来将我们的方法扩展到一般的非对称牛顿多边形，并证明了引理，这将纽顿多角$ a $ a $ a $ a $ a $ a $ a的共轭类别分类。
We notice a remarkable connection between Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations. As an application of the new formalism we show how to construct integrable system with spectral curve with arbitrary symmetric Newton polygon. Finally, we embed this integrable system into double Bruhat cell of a Poisson-Lie group, show how triangular decomposition can be used to extend our approach to general non-symmetric Newton polygons, and prove Lemma, which classifies conjugacy classes in double affine Weyl groups of $A$-type by Newton polygons.
