Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras
The aim of this paper is to prove the existence of the strong Bernstein- Gel'fand-Gel'fand (BGG) resolution for arbitrary Kac-Moody algebras, known up to now for the symmetrizable case [\textit{I. N. Bernstein, I. M. Gel'fand} and \textit{S. I. Gel'fand}, Lie groups Represent., Proc. Summer Sch. Bolyai János Math. Soc., Budapest 1971, 21-64 (1975; Zbl 0338.58019); \textit{H. Garland} and \textit{J. Lepowsky}, Invent. Math. 34, 37- 76 (1976; Zbl 0358.17015); \textit{G. Kempf}, Adv. Math. 29, 310-396 (1978; Zbl 0393.20027)]. Some standard consequences of the BGG resolution are given. In particular, the author obtains Konstant's theorem on ``\({\mathfrak n}\)-homology'' for arbitrary Kac-Moody algebras (known so far only in the symmetrizable case).
scientific article; zbMATH DE number 4152654
scientific article