Irreducible representations of $\GL(g,\C)$ (awaiting review)

The irreducible finite-dimensional representations of $\GL(g,\C)$ correspond bijectively to the $g$-tuples of integers $(\lambda_1,\ldots,\lambda_g)$ with $\lambda_1\geqslant \lambda_2\geqslant\ldots\geqslant \lambda_g$ ( highest weight of the representation) . For example the determinant representation corresponds to the $g$-tuple $\lambda_1=\ldots=\lambda_g=1$.