Twining characters, Konstant's homology formula, and the Bernstein-Gelfand-Gelfand resolu\-tion. (Q1872572)

The author gives a new proof for the formula for the twining character of the Verma module with symmetric highest weight and for the formula for the twining character of the irreducible highest module with symmetric dominant integral highest weight over a symmetrizable generalized Kac-Moody algebra. The original result was obtained in [\textit{J. Fuchs}, \textit{U. Ray} and \textit{C. Schweigert}, J. Algebra 191, No. 2, 518--540 (1997; Zbl 0885.17016)] and [\textit{J. Fuchs}, \textit{B. Schellekens} and \textit{C. Schweigert}, Commun. Math. Phys. 180, No. 1, 39--97 (1996; Zbl 0863.17020)]. The approach presented in the paper under review is based on the existence of a Bernstein-Gelfand-Gelfand resolution, constructed in [\textit{S. Naito}, Publ. Res. Inst. Math. Sci. 29, No. 4, 709--730 (1993; Zbl 0822.17022)].