On the behaviour of unipotent elements from subsystem subgroups of small ranks in irreducible representations of the classical algebraic groups in positive characteristic

Аннотация:
The behaviour of unipotent elements from subsystem subgroups of small ranks in modular irreducible representations of the classical algebraic groups is investigated. In the talk, the principal attention will be given to regular unipotent elements from subsystem subgroups of type $A_5$ and $C_3$ in representations of groups of type $A_n$ and $C_n$, respectively. For infinitesimally irreducible representations, it is proved that the images of such elements have Jordan blocks of all a priori possible sizes if some 10 consecutive coefficients of the highest weight in the first case and last 6 consecutive coefficients of this weight in the second one satisfy certain special conditions. These are joint results with T. S. Busel.