Wei-Norman equations for classical groups via cominuscule induction

TL;DR

This paper introduces a method to simplify Wei-Norman equations for classical Lie groups into a hierarchy of matrix Riccati equations using cominuscule induction, with special handling for exceptional Lie algebras.

Contribution

It extends the reduction of Wei-Norman equations to Riccati form for all classical groups and provides a new hierarchy for exceptional Lie algebras.

Findings

Reduction of Wei-Norman equations to Riccati equations for classical groups

Hierarchy of nonlinear equations for exceptional Lie algebras

Applicable to all reductive Lie algebras except G2, F4, E8

Abstract

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.