On the Spaltenstein correspondence.
type: Item
instance of: scholarly article
title: On the Spaltenstein correspondence.
zbMATH Open document ID: 1064.14057
DOI: 10.1016/S0019-3577(04)90008-0
author: Ngoc Gioan Jean Pagnon
published in: Indagationes Mathematicae. New Series
publication date: 2005-01-03T00:00:00Z
review text: Let \(M(n,k)\) be the \(n\times n\)-matrices with entries in an algebraically closed field \(k\) and let \(V\) be a vector space over \(k\) of dimension \(n\). \textit{N. Spaltenstein} [Nederl. Akad. Wet., Proc., Ser. A 79, 452--456 (1976; Zbl 0343.20029)] established a bijection between the irreducible components of the space of full flags \(\mathcal F_x\) fixed by a nilpotent element \(x\in M(n,k)\) and the standard tableaux associated to the Young diagram of \(x\). The main result of the present article is to determine, when \(x\) is of hook type, for each irreducible component \(X\) of \(\mathcal F_x\), the unique Schubert cell \(\mathcal C_X\) of the full flag manifold \(\mathcal F(V)\), such that \(\mathcal C_X\cap X\) is a dense subspace of \(X\).
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 2124632
zbMATH Keywords: flag manifolds
zbMATH Keywords: nilpotent element
zbMATH Keywords: standard tableaux
zbMATH Keywords: Young diagram
zbMATH Keywords: Schubert cell
zbMATH Keywords: hook type
zbMATH Keywords: irreducible components
reviewed by: Dan Laksov
MaRDI profile type: Publication
cites work: Singular loci of Schubert varieties
cites work: Representations of Coxeter groups and Hecke algebras
cites work: Q3860031
cites work: Q4112123
cites work: On the fixed point set of a unipotent element on the variety of Borel subgroups
cites work: Q3677929
cites work: Q5592048
cites work: Q5587150
cites work: Q3907682
description: scientific article; zbMATH DE number 2124632