Singular components of Springer fibers in the two-column case
Annales de l'Institut Fourier, Volume 59 (2009) no. 6, pp. 2429-2444.

We consider the Springer fiber 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 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 u .

On considère la fibre de Springer u pour un endomorphisme nilpotent u tel que u 2 =0. On décrit les éléments des composantes de 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 u .

DOI: 10.5802/aif.2495
Classification: 14M15, 14B05
Keywords: Flag varieties, Springer fibers, singularity criteria, Young tableaux
Mot 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, Volume 59 (2009) no. 6, pp. 2429-2444. doi : 10.5802/aif.2495. http://archive.numdam.org/articles/10.5802/aif.2495/

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