Demazure Character Formulas for Generalized Kac--Moody Algebras

Abstract

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

23 pages