Categories of nonstandard highest weight modules for affine Lie algebras
type: Item
instance of: scholarly article
title: Categories of nonstandard highest weight modules for affine Lie algebras
zbMATH Open document ID: 0851.17025
DOI: 10.1007/PL00004513
published in: Mathematische Zeitschrift
publication date: 1996-05-19T00:00:00Z
full work available at URL: https://eudml.org/doc/174844
review text: This paper makes an important contribution towards the representation theory of affine Kac-Moody Lie algebras, building on previous work of Cox, Futorny and Saifi. The authors consider nonstandard generalized Verma modules, i.e. generalized Verma modules induced from a nonstandard Borel subalgebra. In the case of nonzero central charge, they prove that any such module is generated by the sum of its finite-dimensional weight spaces. They then classify the submodules, and use this information to construct a generalized strong BGG resolution. The authors then consider certain full subcategories of the category of weight modules over the affine Lie algebra. These subcategories, called ``truncated'' categories, contain the nonstandard generalized Verma modules. The authors establish an equivalence of categories between this truncated category and a category of modules for a subalgebra of the original affine Lie algebra. Using results about the latter category obtained by Rocha and Wallach, they prove BGG duality for the truncated category.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B55
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 861945
zbMATH Keywords: nonstandard highest weight modules
zbMATH Keywords: representation
zbMATH Keywords: affine Kac-Moody Lie algebras
zbMATH Keywords: nonstandard generalized Verma modules
zbMATH Keywords: generalized strong BGG resolution
zbMATH Keywords: truncated category
zbMATH Keywords: BGG duality
author: Ben Cox
author: Vyacheslav Futorny
author: Duncan J. Melville
reviewed by: Murray R. Bremner
MaRDI profile type: Publication
OpenAlex ID: W2026956638
description: scientific article; zbMATH DE number 861945