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arXiv · 1307.6132

Separation coordinates, moduli spaces and Stasheff polytopes

Konrad Schöbel·Alexander P. Veselov
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Abstract

We show that the orthogonal separation coordinates on the sphere $S^n$ are naturally parametrised by the real version of the Deligne-Mumford-Knudsen moduli space $\bar M_{0,n+2}(R)$ of stable curves of genus zero with $n+2$ marked points. We use the combinatorics of Stasheff polytopes tessellating $\bar M_{0,n+2}(R)$ to classify the different canonical forms of separation coordinates and deduce an explicit construction of separation coordinates and Stäckel systems from the mosaic operad structure on $\bar M_{0,n+2}(R)$.

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Konrad Schöbel, Alexander P. Veselov. 2014-01-16. Separation coordinates, moduli spaces and Stasheff polytopes. https://arxiv.org/abs/1307.6132

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