REPRESENTATIONS OF MODULAR LIE-ALGEBRAS THROUGH QUANTUM GROUPS

Let g be the Lie algebra of a simple, simply-connected algebraic group over the field of p elements, and let U(p) (g underbar) be its (non-r estricted) enveloping algebra. When g underbar is of type A(n), C(n) o r D4, we construct irreducible representations of U(p) (g underbar) of dimension p(d), where d is half the dimension of a minimal orbit in t he associated complex simple Lie algebra. The representations are obta ined by specializing representations of quantum groups at roots of uni ty.