Universal Verma modules and \(W\)-resolvents over Kac-Moody algebras
The paper under review presents a systematic exposition of various questions in the theory of extremal equations over Kac-Moody algebras. The main aim of this theory is to derive precise formulae for all primitive elements of Verma modules over Lie algebras with triangular decomposition. The present paper is mostly a survey about new methods which allow one to reproduce classical finite-dimensional results and which can also be applied to infinite-dimensional Lie algebras. The author describes some special extensions of the universal enveloping algebras, investigates the structure of \(W\)-resolvents and uses these methods for the study of extremal projectors over Kac-Moody algebras. The main result of the paper gives a precise formula for extremal projectors associated with Kac-Moody algebras. This formula is written in combinatorial terms, which use only combinatorics of the Weyl group.
scientific article; zbMATH DE number 1535337