CHARACTERS OF MODULAR TORSION-FREE REPRESENTATIONS OF CLASSICAL LIE-ALGEBRAS

In this paper, we analyze the characters of modular, irreducible representations of classical Lie algebras g of types A(l-1) and C(l) arising from a characteristic 0 construction of torsion free representations. By character, we refer to linear functionals on g identified with algebra homomorphisms from a distinguished central subalgebra O of the universal enveloping algebra of g. If Lie(G) = g, then for each character chi, standard representatives with respect to a fixed toral subalgebra are found in the G-orbit containing the character chi. For many parameters, these characters are nilpotent. Furthermore, modular representations of type A(l-1) and type C(l) Lie algebras constructed by induction from these irreducible, torsion free representations are shown to admit characters in a family of both Richardson and non-Richardson nilpotent orbits. Through this explicit induction construction, irreducible representations of minimal p-power dimension under the Kac-Weisfeiler conjecture are realized.