Abstract
We introduce a family of -submodules V
w
(λ) of the irreducible highest weight U
q
(𝔤)-module V(λ) of dominant integral highest weight λ for a generalized Kac–Moody algebra 𝔤. We prove that the module V
w
(λ) is spanned by its global basis, and then give a character formula for V
w
(λ), which generalizes the Demazure character formula for ordinary Kac–Moody algebras.
ACKNOWLEDGMENTS
The author is grateful to Professor Satoshi Naito for reading the manuscript very carefully and for valuable comments. He is also grateful to Professor Daisuke Sagaki for valuable comments.
Notes
Communicated by K. Misra.