In this research the principal investigator will pursue further the representation theory of general linear groups. In particular, there is good reason to suppose that new light can be shed on the classical theory of representations in the describing characteristic by subsuming this theory as a special case of the constructions of the principal investigator and his coworker. The major goal of the proposed work is to investigate other classical groups extending the techniques developed by the principal investigator in previous work, with the aim of obtaining a classification of the simple representations of these groups. For this, Hecke algebras associated with Weyl groups have to be studied. In view of the key role of these algebras in the whole field this might be of interest by itself, providing more detailed information on Hecke algebras applicable to related topics.
