Separation coordinates, moduli spaces and Stasheff polytopes

2013/07/23 by Schöbel, Konrad, Veselov, Alexander P. · 1 citation
#14H10 #53A60 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1307.6132

Abstract

We show that the orthogonal separation coordinates on the sphere Sⁿ are naturally parametrised by the real version of the Deligne-Mumford-Knudsen moduli space M_0,n+2(R) of stable curves of genus zero with n+2 marked points. We use the combinatorics of Stasheff polytopes tessellating 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 M_0,n+2(R).

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