WEIGHTS OF INFINITESIMALLY IRREDUCIBLE REPRESENTATIONS OF CHEVALLEY GROUPS OVER A FIELD OF PRIME CHARACTERISTIC

Abstract

Let be an algebraically closed field of characteristic , a universal Chevalley group over with an irreducible root system , a basis of , the set of radical weights that are nonnegative with respect to the natural ordering associated with , the set of dominant weights, and the maximum of the squares of the ratios of the lengths of the roots in . It is well known that if is of type , , , , or , if is of type , , or , and if is of type . A rational representation is called infinitesimally irreducible if its differential defines an irreducible representation of the Lie algebra of the group . Let be a simple complex Lie algebra with the same root system as . In this paper it is proved that for the system of weights of an infinitesimally irreducible representation of a group with highest weight coincides with the system of weights of an irreducible complex representation of a Lie algebra with the same highest weight. In particular, the set of dominant weights of the representation is . Bibliography: 7 titles.