Singular components of Springer fibers in the two-column case

Fresse, Lucas

doi:10.5802/aif.2495

Singular components of Springer fibers in the two-column case
[Composantes singulières des fibres de Springer dans le cas deux-colonnes]

Fresse, Lucas ¹

¹ Weizmann Institute of Science Department of Mathematics Rehovot 76100 (Israel)

Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2429-2444.

Résumé
Abstract

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 $ℬ_{u}$ .

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 $ℬ_{u}$ .

MR Zbl | 2 citations dans Numdam

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

Affiliations des auteurs :

Fresse, Lucas ¹

¹ Weizmann Institute of Science Department of Mathematics Rehovot 76100 (Israel)

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     title = {Singular components of {Springer} fibers in the two-column case},
     journal = {Annales de l'Institut Fourier},
     pages = {2429--2444},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {59},
     number = {6},
     year = {2009},
     doi = {10.5802/aif.2495},
     zbl = {1191.14060},
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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. http://www.numdam.org/articles/10.5802/aif.2495/

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