Irreducible modules of sl_mp in characteristic p with regular or subregular nilpotent p-characters

Let K be an algebraically closed field of prime characteristic p. If p does not divide n, irreducible modules over sl_n(K) for regular and subregular nilpotent representations have already known (see [10] and [9]). In this article, we investigate the question when p divides n, and precisely describe simple modules of sl_n for regular and subregular nilpotent representations.