1307.6132 (Konrad Schöbel et al.)

Separation coordinates, moduli spaces and Stasheff polytopes    [PDF]

Konrad Schöbel, Alexander P. Veselov

We show that the 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 St\"ackel systems from the mosaic operad structure on $\bar M_{0,n+2}(R)$.

View original: http://arxiv.org/abs/1307.6132