Twining characters, Kostant’s homology formula, and the Bernstein- Gelfand-Gelfand resolution

Abstract

We give a new proof of the formulas for the twining character of the Verma module $M(\lambda )$ of symmetric highest weight $\lambda$ and for the twining character of the irreducible highest weight module $L(\Lambda )$ of symmetric, dominant integral highest weight $\Lambda$ over a symmetrizable generalized Kac-Moody algebra g, by using the Bernstein-Gelfand-Gelfand resolution of $L(\Lambda )$.