In [1] the authors studied irreducible highest weight representations of the simple n-Lie algebra. However, as was pointed out to us by X. Garcia-Martinez, R. Turdibaev, T. van der Linden in [2], Proposition 1 and the results of Section 2 do not hold unless we impose the extra assumption the the n-Lie algebra V is such that

$$ \tilde{\mathrm{ad}}:{\wedge}^{n-1}V\to \wedge \bullet V $$

is skew-symmetric. For the simple n-Lie algebra this condition is automatically satisfied, hence the main results of the paper are correct.

We thank X. Garcia-Martinez, R. Turdibaev, T. van der Linden for pointing out this mistake to us.