Decomposition numbers of finite groups of Lie type in non-defining characteristic

Abstract

In 1982 P. Fong and B. Srinivasan published a paper [12] on the blocks of the finite general linear and unitary groups, which revealed the surprising fact that block theory and Deligne-Lusztig theory are highly compatible for these groups. Since then a lot of work has been done on the l-modular character theory of groups of Lie type where l is a prime different from the underlying characteristic of the group. In this survey article I shall present some of these results. I shall concentrate on those which are general in the sense that they can be formulated and proved for all groups of Lie type and not just for a particular series such as the general linear groups.