Filtration and splitting of the Hodge bundle on the non-varying strata of quadratic differentials

We describe the Harder–Narasimhan filtration of the Hodge bundle for Teichmüller curves in the non-varying strata of quadratic differentials appearing in [CM2]. Moreover, we show that the Hodge bundle on the non-varying strata away from the irregular components can split as a direct sum of line bundles. As applications, we determine all individual Lyapunov exponents of algebraically primitive Teichmüller curves in the non-varying strata and derive new results regarding the asymptotic behavior of Lyapunov exponents.