Submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules
type: Item
instance of: scholarly article
title: Submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules
zbMATH Open document ID: 0908.17004
DOI: 10.1023/A:1009929615175
author: Volodymyr Mazorchuk
author: S. Ovsienko
published in: Algebras and Representation Theory
publication date: 1999-03-14T00:00:00Z
review text: This paper gives a generalization of the Bernstein, Gelfand, and Gelfand description of the submodule structure of Verma modules in terms of the Weyl group action on infinitesimal characters. The Lie algebras under study in this paper are \({\mathfrak {sl}}(n,{\mathbb C})\), and the generalized Verma modules studied are the ones induced from so-called generic Gelfand-Zetlin modules over the standard upper left hand corner inclusion of \({\mathfrak {sl}}(k,{\mathbb C})\) into \({\mathfrak {sl}}(n,{\mathbb C})\).
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 1186172
zbMATH Keywords: special linear Lie algebras
zbMATH Keywords: Bernstein, Gelfand, and Gelfand description
zbMATH Keywords: submodule structure
zbMATH Keywords: Weyl group action
zbMATH Keywords: generalized Verma modules
zbMATH Keywords: Gelfand-Zetlin modules
reviewed by: Mark R. Sepanski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1186172