Robinson-Schensted-type algorithms for the spinor representations of the orthogonal Lie algebra \({\mathfrak so}(2n,\mathbb{C})\)
type: Item
instance of: scholarly article
title: Robinson-Schensted-type algorithms for the spinor representations of the orthogonal Lie algebra \({\mathfrak so}(2n,\mathbb{C})\)
zbMATH Open document ID: 0814.17006
author: Soichi Okada
published in: Journal of Algebra
publication date: 1993-08-25T00:00:00Z
review text: The ordinary representation theory of the classical linear groups, arising from the intertwining action of appropriate symmetric groups, devolves on the manipulation of Young diagrams and Young tableaux. There is an extension of spinor representations which requires the addition of half boxes to the usual diagrams. Furthermore, there is a subset of the set of all tableaux, called semi-standard tableaux, in which the tableaux entries are strictly increasing down columns but weakly increasing along rows. In this paper the author extends the so-called Robinson-Schensted algorithm for the manipulation of semi-standard tableaux, which may be used to reduce certain representations, to encompass the spinor representations of the orthogonal algebra \({\mathfrak {so}}( 2n,\mathbb{C})\).
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 218575
zbMATH Keywords: Young diagrams
zbMATH Keywords: Robinson-Schensted algorithm
zbMATH Keywords: semi-standard tableaux
zbMATH Keywords: spinor representations
reviewed by: N. B. Backhouse
MaRDI profile type: Publication
full work available at URL: jabr.1993.1129
OpenAlex ID: W1993594440
Wikidata QID: Q115396308
DOI: 10.1006/JABR.1993.1129
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description: scientific article; zbMATH DE number 218575