Abstract. Let K be an algebraically closed field of characteristic p > 0 and let Sp(2m) be the symplectic group of rank m over K. The main theorem of this article gives the character of the rational simple Sp(2m)-modules with fundamental highest weight as an explicit alternating sum of characters of Weyl modules. One obtains several formulae for the dimensions of these simple modules, what allo...

We give a sufficient criterion on a highest weight module of a semisimple Lie algebra to admit a resolution in terms of sums of modules induced from a parabolic subalgebra. In particular, we show that all unitary highest weight modules admit such a resolution. As an application of our results we compute (minimal) resolutions and explicit formulas for the Hilbert series of the unitary highest we...

In a Borel subalgebra U(B) of the sl2 loop algebra, we introduce a highest weight vector Ψ. We call such a representation of U(B) that is generated by Ψ highest weight. We define a generalization of the Drinfeld polynomial for a finitedimensional highest weight representation of U(B). We show that every finitedimensional highest weight representation of the Borel subalgebra is irreducible if th...