Small degree representations of finite Chevalley groups in defining characteristic

Abstract: The author has determined, for all simple simply connected reductive linear algebraic groups defined over a finite field, all the irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l, this bound is proportional to l³, and for rank less than or equal to 11 much higher. The small rank cases are based on extensive computer calculations.