Olivier Mathieu, Georges Papadopoulo. 
A combinatorial character formula for some highest weight modules.

Abstract : We give a combinatorial formula for the weight multiplicities of 
some infinite dimensional highest weight {\goth
gl}$(n)$-modules. Our proof, which does not rely on Kazdhan-Lusztig 
combinatorics, uses a reduction to finite characteristics. The
character formula for the corresponding modular representations, which has 
been computed in {\bf [MP]}, is based on a dual pair
which has no obvious counterpart in characteristic zero.