Decomposition numbers and Cartan invariants of finite groups of Lie type in the defining characteristic.

摘要

In this thesis we investigate the problem of finding the decomposition numbers and Cartan invariants of some finite groups of Lie type of small rank in the defining characteristic 2.;The groups that we consider here are the 4-dimensional symplectic group, and 3-dimensional special linear and special unitary groups over finite fields of characteristic 2. We use some results of Chastkofsky and Feit on the principal indecomposable characters of these groups to obtain all the decomposition numbers corresponding to unipotent characters of the above mentioned groups. This will lead to determination of some other decomposition numbers and specific Cartan invariants in characteristic 2.