On some Lie-theoretic solutions of the tt-Toda equations with integer Stokes data

We describe some solutions of the tt*-Toda equations with integer Stokes data, based on a Lie-theoretic approach. In particular, we find all such solutions in a certain 1-parameter family. For general solutions, we compare the results of Guest–Its–Lin (based on solving the equations) with the original classification of Cecotti–Vafa (based on braid group orbits of Stokes matrices for hypothetical solutions), and find that these agree in low dimensions.