Penkov, Ivan; Zuckerman, Gregg Construction of generalized Harish-Chandra modules with arbitrary minimal \(\mathfrak k\)-type. (English) Zbl 1173.17010 Can. Math. Bull. 50, No. 4, 603-609 (2007). This paper is a part of the project whose ultimate goal is the classification of simple generalized Harish-Chandra modules over a semisimple finite-dimensional complex Lie algebra \(\mathfrak g\) (i.e. infinite-dimensional modules having finite-dimensional isotypic components as a module over some reductive subalgebra \(\mathfrak k\)).From the abstract: “For any simple finite dimensional \(\mathfrak k\)-module \(V\), we construct simple \((\mathfrak g, \mathfrak k)\)-modules \(M\) with finite dimensional \(\mathfrak k\)-isotypic components such that \(V\) is a \(\mathfrak k\)-submodule of \(M\) and the Vogan norm of any simple \(\mathfrak k\)-submodule \(V^\prime \subset M\), \(V^\prime \not\simeq V\), is greater than the Vogan norm of \(V\)”. Reviewer: Pasha Zusmanovich (Reykjavik) Cited in 4 Documents MSC: 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B55 Homological methods in Lie (super)algebras Keywords:generalized Harish-Chandra module; isotypic component; Vogan norm PDFBibTeX XMLCite \textit{I. Penkov} and \textit{G. Zuckerman}, Can. Math. Bull. 50, No. 4, 603--609 (2007; Zbl 1173.17010) Full Text: DOI arXiv