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We review how some multianalytic inner functions of the Beurling type theoremare associated to row contractions following works of G.Popescu. Motivated by aresult on weak Markov dilations, we define a notion of characteristic functionfor ergodic and coisometric row contractions with a one-dimensional invariantsubspace for the adjoints. Our characteristic function is a complete unitaryinvariant for such tuples. Thereafter we extend the analysis of characteristicfunctions to contractive liftings of row contractions. We apply our theory tocompletely positive maps and explore applications to fixed point sets ofcompletely positive maps related to each other by a subisometric lifting. Inthe last two chapter we consider constrained row contractions and some modulestructures in this context.

Characteristic Functions, Liftings and Modules