We introduce a family of U-q(+) (g)-submodules V-w(lambda) of the irreducible highest weight U-q(g)- module V(lambda) of dominant integral highest weight lambda for a generalized Kac-Moody algebra g. We prove that the module V-w(lambda) is spanned by its global basis, and then give a character formula for V-w(lambda), which generalizes the Demazure character formula for ordinary Kac- Moody algebras.
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