%0 Journal Article %T Some Infinite Dimensional Representations of Reductive Groups with Frobenius Maps %A Nanhua Xi %J Mathematics %D 2013 %I arXiv %R 10.1007/s11425-014-4818-y %X In this paper we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps. In particular, a few classical results of Steinberg and Deligne & Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps. %U http://arxiv.org/abs/1312.1159v3