Universal Verma modules and \(W\)-resolvents over Kac-Moody algebras
type: Item
instance of: scholarly article
title: Universal Verma modules and \(W\)-resolvents over Kac-Moody algebras
zbMATH Open document ID: 0980.17013
DOI: 10.1007/BF02551242
author: D. P. Zhelobenko
published in: Theoretical and Mathematical Physics
publication date: 2000-11-23T00:00:00Z
review text: 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.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 1535337
zbMATH Keywords: extremal projector
zbMATH Keywords: symmetrizable Kac-Moody algebra
zbMATH Keywords: resolution
zbMATH Keywords: Verma module
zbMATH Keywords: hyper-symmetry
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1535337