An occurrence of the Robinson-Schensted correspondence
type: Item
instance of: scholarly article
title: An occurrence of the Robinson-Schensted correspondence
zbMATH Open document ID: 0653.20039
DOI: 10.1016/0021-8693(88)90177-9
author: Robert Steinberg
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let \({\mathcal F}\) be the flag manifold of an \(n\)-dimensional vector space \(V\). To each unipotent transformation \(u\) of \(V\), denote by \({\mathcal F}_ u\) the variety of flags fixed by \(u\). In this paper it is shown that the element of \(S_ n\) which determines the relative position of two irreducible components is equal to the element given by the Robinson-Schensted correspondence applied to the associated two standard tableaux. As pointed out by the author a proof of this result has also been given by \textit{N. Spaltenstein} [in: Classes unipotentes et sous groupes de Borel. Lect. Notes Math. 946. Berlin etc.: Springer Verlag (1982; Zbl 0486.20025)] although the Robinson-Schensted process is there only implicit.
reviewed by: Henning Haahr Andersen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 20B20
zbMATH DE Number: 4065283
zbMATH Keywords: flag manifold
zbMATH Keywords: unipotent transformation
zbMATH Keywords: variety of flags
zbMATH Keywords: irreducible components
zbMATH Keywords: Robinson-Schensted correspondence
zbMATH Keywords: standard tableaux
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90177-9
OpenAlex ID: W1981735132
cites work: Permutations, matrices, and generalized Young tableaux
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description: scientific article; zbMATH DE number 4065283