On -Kostka numbers and Young modules

The combinatorial properties of Young modules corresponding to maximal Young subgroups are studied: an explicit formula for p -Kostka numbers is given, and as applications, the ordinary characters of Young modules are described and a branching rule for Young modules is determined. Moreover, for certain n -part partitions the reduction formulas for p -Kostka numbers given in A. Henke, S. Koenig [Relating polynomial G L n -representations in different degree, J. Reine Angew. Math. 551 (2002) 219] are reproved.