Jordan algebras and generalized principal series representations
type: Item
instance of: scholarly article
title: Jordan algebras and generalized principal series representations
zbMATH Open document ID: 0829.22023
DOI: 10.1007/BF01444516
author: Genkai Zhang
published in: Mathematische Annalen
publication date: 1996-01-17T00:00:00Z
full work available at URL: https://eudml.org/doc/165352
review text: Let \(N\) be a semisimple Jordan algebra and let \(G\) be the group of conformal transformations of \(N\) and \(P\) the Poincaré group. We study certain induced representations of \(G\) from \(P\) and calculate the composition series in the compact picture. We find the Hermitian norm on each \(K\)-type. This generalizes recent results of \textit{K. D. Johnson} [Math. Ann. 287, 703-718 (1991; Zbl 0702.22017)] and of \textit{E. Kostant} and \textit{S. Sahi} [Adv. Math. 87, 71-92 (1991; Zbl 0748.22008)]. The author was informed by \textit{S. Sahi} that he has also obtained most of the above mentioned results in [Jordan algebras and degenerate principal series (to appear)].
reviewed by: Genkai Zhang
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 17C20
Mathematics Subject Classification ID: 17C30
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 43A90
zbMATH DE Number: 800588
zbMATH Keywords: Jordan algebras
zbMATH Keywords: generalized principal series representations
zbMATH Keywords: Lie algebra
zbMATH Keywords: conformal group
zbMATH Keywords: Poincaré group
zbMATH Keywords: composition series
zbMATH Keywords: Hermitian norm
MaRDI profile type: Publication
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OpenAlex ID: W2082905088
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description: scientific article; zbMATH DE number 800588