Mathematics

The generalized hypergeometric function mFm-1 is the "closest relative" of the famous hypergeometric function of Gauss-Riemann. The rational Calogero-Mozer system is an integrable system of point-particles on the real line, which appears in a surprisingly vast array of different and seemingly unrelated areas of Mathematics. In this talk, I will show that a flow of the Calogero-Mozer system generates a symmetry of mFm-1. Applications of the symmetry include a non-trivial action of the quaternions on the direct sum of the solution space of the generalized hypergeometric equation and its dual and an elliptic generalization of Cauchy identity.