Correspondence between $\mathfrak{sl}(n,\mathbb{C})$ and $\mathfrak{gl}(n,\mathbb{C})$ representations

Question

There is a one-to-one correspondence between irreducible $\mathfrak{gl}(n,\mathbb{C})-$representations and $\mathbb{C} \times \{ \text{irreducible } \mathfrak{sl}(n,\mathbb{C}) \text{ representations} \}.$

I'm having difficulty forming an explicit map between these two sets. Any ideas would be much appreciated.