no. 6
Singular components of Springer fibers in the two-column case
[Composantes singulières des fibres de Springer dans le cas deux-colonnes]
Fresse, Lucas1
1 Weizmann Institute of Science Department of Mathematics Rehovot 76100 (Israel)
Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2429-2444

We consider the Springer fiber ℬ u corresponding to a nilpotent endomorphism u of nilpotent order 2. As a first result, we give a description of the elements of a given component of ℬ u which are fixed by the action of the standard torus relative to some Jordan basis of u. By using this result, we establish a necessary and sufficient condition of singularity for the components of ℬ u .

On considère la fibre de Springer ℬ u pour un endomorphisme nilpotent u tel que u 2 =0. On décrit les éléments des composantes de ℬ u qui sont fixés par l’action du tore standard relatif à une base de Jordan de u. À l’aide de ce résultat, on établit une condition nécessaire et suffisante de singularité pour les composantes de ℬ u .

DOI : 10.5802/aif.2495
Classification : 14M15, 14B05
Keywords: Flag varieties, Springer fibers, singularity criteria, Young tableaux
Mots-clés : variétés de drapeaux, fibres de Springer, critères de singularité, tableaux de Young

Fresse, Lucas 1

1 Weizmann Institute of Science Department of Mathematics Rehovot 76100 (Israel) 
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Fresse, Lucas. Singular components of Springer fibers in the two-column case. Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2429-2444. doi: 10.5802/aif.2495

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