Reducibility modulo p of complex representations of finite groups of lie type: Asymptotical result and small characteristic cases

Let G be a finite group of Lie type in characteristic p. This paper addresses the problem of describing the irreducible complex (or p-adic) representations of G that remain absolutely irreducible under the Brauer reduction modulo p. An efficient approach to solve this problem for p > 3 has been elaborated in earlier papers by the authors. In this paper, we use arithmetical properties of character degrees to solve this problem for the groups G ∈ {²B₂(q), ²G₂(q), G₂(q), ²F₄(q), F₄(q), ³D₄(q)} provided that p ≤ 3. We also prove an asymptotical result, which solves the problem for all finite groups of Lie type over double-struck F sign_q with q large enough.