论文标题
格拉斯曼尼亚人的循环对称基因座
Cyclic symmetry loci in Grasssmannians
论文作者
论文摘要
格拉斯曼尼亚人通过循环移位图承认有限循环群的作用。我们简单地描述了该循环基团的每个元素固定的点，从而扩展了KARP对循环移位本身固定的点的描述。我们给出了每个环状对称基因座中完全非负点的一组细胞分解，并描述有效的总阳性测试，将后尼科夫的结果扩展到周期性对称的设置。我们描述了循环对称基因座上的一个猜想的广义群集结构，前提是Orbifold点的顺序足够大。我们发现的广义交流关系应该是用于研究TeichmüllerOrbifolds理论的Chekhov和Shapiro的较高的Teichmüller类似物。
The Grassmannian admits an action by a finite cyclic group via the cyclic shift map. We give a simple description of the points fixed by each element of this cyclic group, extending Karp's description of the points fixed by the cyclic shift itself. We give a cell decomposition of the set of totally nonnegative points in each cyclic symmetry locus and describe efficient total positivity tests, extending results of Postnikov to the cyclically symmetric setting. We describe a conjectural generalized cluster structure on cyclic symmetry loci provided the order of the orbifold point is sufficiently large. The generalized exchange relations we find should be a Higher Teichmüller analogue of the relations Chekhov and Shapiro used to study Teichmüller theory of orbifolds.
