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Grassmannian-parameterized solutions to direct-sum polygon and simplex equations
Journal of Mathematical Physics ( IF 1.2 ) Pub Date : 2021-05-03 , DOI: 10.1063/5.0035760
Aristophanes Dimakis 1 , Igor G. Korepanov 2
Affiliation  

We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang–Baxter (2-simplex), respectively. We examine the general structure of (2n + 1)-gon and 2n-simplex equations in direct sums of vector spaces. Then, we provide a construction for their solutions, parameterized by elements of the Grassmannian Gr(n + 1, 2n + 1).

中文翻译:

直接求和多边形和单纯形方程的 Grassmannian 参数化解

我们考虑多边形和单纯形方程,其中最简单的非平凡例子分别是五边形(5-gon)和 Yang-Baxter(2-单纯形)。我们在向量空间的直接和中检查 (2 n + 1)-gon 和 2 n -单纯形方程的一般结构。然后,我们为他们的解决方案提供了一个构造,由 Grassmannian Gr( n + 1, 2 n + 1)的元素参数化。
更新日期:2021-05-28
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