Thermodynamical limit of general gl(N) spin chains: vacuum state and densities

We study the vacuum state of spin chains where each site carry an arbitrary representation. We prove that the string hypothesis, usually used to solve the Bethe ansatz equations, is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the center of the strings for the vacuum. We work out different examples and, in particular, the spin chains with periodic array of impurities.