For a dominant integral weight $lambda $, we introduce a family of $U_q ^+ (mathfrak{ g})$-submodules $V_w (lambda)$ of the irreducible highest weight $U_q (mathfrak{ g})$-module $V(lambda)$ of highest weight $lambda $ for a generalized Kac--Moody algebra $mathfrak{ g}$. 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.
Categories: math.RT math.QA