Nanhua Xi: Some infinite dimensional representations of reductive groups with Frobenius maps

We use Frobenius’s construction of induced modules to study representations of algebraic groups with Frobenius maps. This construction gives rise to some (abstract) irreducible infinite dimensional representations of algebraic groups with Frobenius maps. In particular, a few classical results on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.