Induction, deformation, and specialization of Lie algebra representations
type: Item
instance of: scholarly article
title: Induction, deformation, and specialization of Lie algebra representations
zbMATH Open document ID: 0714.17008
DOI: 10.1007/BF01459255
author: Eric M. Friedlander
author: Brian J. Parshall
published in: Mathematische Annalen
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/164828
review text: The authors continue their recent study of non-restricted representations of restricted Lie algebras. In order to achieve results presented here, they provide a sheaf-theoretic formulation of imprimitivity theory which enables them to consider non-affine orbits of the coadjoint representation. They also introduce deformation and specialization of representations which enable them to formulate conjectural relationships between representations of different character types. Two theorems of particular interest are presented: the first is a complete proof of a result formulated by V. Kac concerning the irreducibility of certain induced characters; the second is a proof of a conjecture of V. Kac and B. Weisfeiler concerning the p-divisibility of the dimensions of representations for the restricted Lie algebra of \(SL_ n\).
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1043
zbMATH Keywords: non-restricted representations
zbMATH Keywords: restricted Lie algebras
zbMATH Keywords: deformation
zbMATH Keywords: specialization
zbMATH Keywords: induced characters
zbMATH Keywords: p-divisibility
zbMATH Keywords: dimensions
Wikidata QID: Q115393435
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1043