Complex representation growth of finite quasisimple groups of Lie type

Abstract

Abstract We give upper bounds to the number of n-dimensional irreducible complex representations of finite quasisimple groups belonging to different families of groups of Lie type. The bounds have the form c ns , where c and s are explicit positive constants that both depend on the family in question. From these bounds, we deduce a uniform bound of the form c n to the number of n-dimensional irreducible representations of all finite quasisimple groups of Lie type. Finally, an application of these results to counting conjugacy classes of maximal subgroups of Lie groups is discussed.