Does anyone have a reference for the rank of Hodge bundles? More precisely, let $X to Y$ be a projective family and let $(mathbb{H}, nabla)$ be a variation of Hodge structure. The Hodge filtration produces a graded bundle: $$mathcal{E}^p : = textbf{R}^{n-p} f_{ast} Omega_{X/Y}^p,$$ where $textbf{R}^{n-p}f_{ast}$ is the right-derived functor of the direct image sheaf and $Omega_{X/Y}^p$ is the sheaf of relative $p$–forms.

**Question:** Is the rank of these vector bundles known?