The sparsity of dimensions of irreducible representations of finite simple groups
The sparsity of dimensions of irreducible representations of finite simple groups
We show that the set of natural numbers which are dimensions of irreducible complex representations of finite quasisimple groups (excluding the natural representations of alternating groups) has density zero. We also determine the exact asymptotics for this set, showing that it has (7 + o(1))x/log x elements less than x. …