Levelt matrices of a hypergeometric family (awaiting review)

The monodromy representation associated to a hypergeometric family is generated by two matrices $h_{\infty}$ and $h_0$ describing the local monodromy around $\infty$ and $0$, respectively. The characteristic polynomial of $h_{\infty}$ is $\prod_j (T - e^{2\pi i \alpha_j})$ and of $h_0$ is $\prod_j (T - e^{2\pi i \beta_j})$, where $(\alpha_j)$ and $(\beta_j)$ are from the defining parameters of the family. The choice of matrices satisfying this condition is determined up to simultaneous conjugacy.

The presentation used here is due to Levelt [MR:0145108].