We develop an inductive approach to the representation theory of the Yokonuma-Hecke algebra ${ \rm Y}_{ d,n}(q)$, based on the study of the spectrum of its Jucys-Murphy elements which are defined here. We give explicit formulas for the irreducible representations of ${ \rm Y}_{ d,n}(q)$ in terms of standard $d$-tableaux; we then use them to obtain a semisimplicity criterion. Finally, we prove the existence of a canonical symmetrising form on ${ \rm Y}_{ d,n}(q)$ and calculate the Schur elements with respect to that form.
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