Wei–Norman equations for classical groups via cominuscule induction

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 G2G2, F4F4 or E8E8. A corresponding hierarchy of nonlinear, albeit no longer Riccati equations, is given for these exceptional cases.