Twining characters and Kostant's homology formula. (Q1411692)

Twining characters of highest weight modules over a symmetrizable generalized Kac-Moody algebra \(\mathfrak{g}\) were introduced in [\textit{J. Fuchs, B. Schellekens} and \textit{C. Schweigert}, Commun. Math. Phys. 180, No. 1, 39--97 (1996; Zbl 0863.17020)]. These characters correspond to automorphisms of Dynkin diagrams. In the paper under review the author uses an extension (to generalized Kac-Moody algebras) of Kostant's homology formula to obtain a formula for twining characters of the homology modules \(H_j(\mathfrak{n}_-,L(\Lambda))\) of the negative part \(\mathfrak{n}_-\) of \(\mathfrak{g}\) with coefficients in some irreducible highest weight module \(L(\Lambda)\). This result is used to obtain a new proof of the formula for the twining character of \(L(\Lambda)\) in the case when \(\Lambda\) is symmetric dominant and integral. This new proof reveals the role, which is played by the subgroup \(\tilde{W}\) of the Weyl group, which consists of all elements, commuting with the Dynkin diagram automorphisms.