Projective representations of generalized reduced enveloping algebras

Let G   be a connected reductive algebraic group over an algebraically closed field of characteristic p>0p>0, and g=Lie(G)g=Lie(G). Let χ∈g⁎χ∈g⁎ be of standard Levi form. In this paper, we study projective representations of Uχs(g)Uχs(g) which is a so-called “higher” reduced enveloping algebra. A reciprocity law on the relation among projective indecomposables, Verma modules and irreducible modules is given. Moreover, a characterization of projective Uχs(g)Uχs(g)-modules in terms of filtrations is given.