A duality theorem for extensions of induced highest weight modules
type: Item
instance of: scholarly article
title: A duality theorem for extensions of induced highest weight modules
zbMATH Open document ID: 0733.17005
author: David H. Collingwood
author: Brad Shelton
published in: Pacific Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let (\({\mathfrak g},{\mathfrak p})\) be a pair consisting of a complex semisimple Lie algebra \({\mathfrak g}\) and its parabolic subalgebra \({\mathfrak p}\). Let also \({\mathfrak p}={\mathfrak l}\oplus {\mathfrak n}\) be a Levi decomposition of \({\mathfrak p}\) with \({\mathfrak l}\) semisimple. The main result is a duality theorem for extensions of induced modules in the category of \({\mathfrak g}\)- modules which are \({\mathfrak l}\)-semisimple and \({\mathfrak p}\)-locally finite. For the proof, the authors transfer the problem into the smooth vetor bundle category where there is a natural duality, the adjoint.
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B66
zbMATH DE Number: 4212273
zbMATH Keywords: Lie algebras of vector fields
zbMATH Keywords: complex semisimple Lie algebra
zbMATH Keywords: parabolic subalgebra
zbMATH Keywords: duality
MaRDI profile type: Publication
full work available at URL: pjm.1990.146.227
OpenAlex ID: W2065311905
DOI: 10.2140/PJM.1990.146.227
description: scientific article; zbMATH DE number 4212273