Wei–Norman equations for classical groups via cominuscule induction

Jan Gutt, Szymon Charzyński, Marek Kuś
2015 Differential geometry and its applications  
We show how to reduce the nonlinear Wei-Norman equations, expressing the solution of a linear system of non-autonomous equations on a Lie algebra, to a hierarchy of matrix Riccati equations using the cominuscule induction. The construction works for all reductive Lie algebras with no simple factors of type G2, F4 or E8. A corresponding hierarchy of nonlinear, albeit no longer Riccati equations, is given for these exceptional cases.
doi:10.1016/j.difgeo.2015.07.001 fatcat:4opcnycoq5cnnh2efkfflmyzy4