THE JORDAN BLOCK STRUCTURE OF THE IMAGES OF UNIPOTENT ELEMENTS IN IRREDUCIBLE MODULAR REPRESENTATIONS OF CLASSICAL ALGEBRAIC GROUPS OF SMALL DIMENSIONS

For unipotent elements of prime order, the Jordan block structure of their images in infinitesimally irreducible representations of the classical algebraic groups in odd characteristic whose dimensions are at most 100, is determined. The approach proposed can be applied for solving a similar problem for representations of bigger dimensions. A detailed information on small cases is important for stating reasonable conjectures on the behavior of unipotent elements in irreducible representations of the classical algebraic groups.