Demazure Character Formulas for Generalized Kac–Moody Algebras

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.

Key Words:

• Crystal
• Demazure character formula
• Demazure module
• Generalized Kac–Moody algebra
• Path model

2010 Mathematics Subject Classification:

• 20G42
• 17B67

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.