Periodic Staircase Matrices and Generalized Cluster Structures
Periodic Staircase Matrices and Generalized Cluster Structures
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DOI：
10.1093/imrn/rnaa148
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发表时间：
2019-12
影响因子：
1
通讯作者：
M. Gekhtman;M. Shapiro;A. Vainshtein
中科院分区：
文献类型：
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作者：
M. Gekhtman;M. Shapiro;A. Vainshtein
众所周知，几何类型的簇结构中的簇变换通常以行列式恒等式为模型，例如短Plücker关系，Desnanot-Jacobi恒等式及其推广。我们提出了一个结构，在广义簇变换的描述中起着类似的作用，并讨论了它的应用，广义簇结构在$GL_n$兼容的Belavin-Drinfeld Poisson-Lie括号的某个子类，在Drinfeld双$GL_n$，和在空间中的周期差分算子。
As is well known, cluster transformations in cluster structures of geometric type are often modeled on determinant identities, such as short Plücker relations, Desnanot–Jacobi identities, and their generalizations. We present a construction that plays a similar role in a description of generalized cluster transformations and discuss its applications to generalized cluster structures in $GL_n$ compatible with a certain subclass of Belavin–Drinfeld Poisson–Lie brackets, in the Drinfeld double of $GL_n$, and in spaces of periodic difference operators.