On the Number of Representations for Simple Lie Groups

The growth rate function $r_N$ counts the number of irreducible representations of simple complex Lie groups of dimension $N$. While no explicit formula is known for this function, previous works have found bounds for $R_N={\sum }_{i=1}^N{r}_i$. In this paper we improve on previous bounds and show that $R_N=O(N)$.