  We exhibit an explicit sufficient condition for the Lyapunov exponents of a
linear cocycle over a Markov map to have multiplicity 1. This builds on work of
Guivarc'h-Raugi and Gol'dsheid-Margulis, who considered products of random
matrices, and of Bonatti-Viana, who dealt with the case when the base dynamics
is a subshift of finite type. Here the Markov structure may have infinitely
many symbols and the ambient space needs not be compact. As an application, in
another paper we prove the Zorich-Kontsevich conjecture on the Lyapunov
spectrum of the Teichm\"uller flow in the space of translation surfaces.
