Modular Representation Of Sl₄

This paper aims to solve the dimensions of simple modules of A3 in algebraically closed field of prime characteristic. According to Kac-Weisfeiler-Friedlander-Parshall Morita equivalence theory on modular representations of reductive Lie algebras, the simple mod-ules of sl4 are divided into 5 classes, according to the classification of nilpotent orbits of Sl4. The dimensions of simple modules in zero nilpotent case(the restricted repre-sentation) had been solved by Jantzen in 1970s, and Friedlander-Parshall's result in the regular nilpotent case and Jantzen's result in subregular nilpotent case solved the prob-lem of calculating the dimensions of simple modules for the two classes. And there is only one case remaining which is of the minimal (non-zero) nilpotent orbit. The aim of the thesis is to attack the remaining problem. The final result is complete and new on the current literature. It makes the basic problem about the irreducible representation of A3 in algebraically closed field of prime characteristic solved completely (p>2).