Singular components of Springer fibers in the two-column case
[Composantes singulières des fibres de Springer dans le cas deux-colonnes]
Fresse, Lucas
Annales de l'Institut Fourier, Tome 59 (2009), p. 2429-2444 / Harvested from Numdam
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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 .

Publié le : 2009-01-01
DOI : https://doi.org/10.5802/aif.2495
Classification:  14M15,  14B05
Mots clés: variétés de drapeaux, fibres de Springer, critères de singularité, tableaux de Young 
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     author = {Fresse, Lucas},
     title = {Singular components of Springer fibers in the two-column case},
     journal = {Annales de l'Institut Fourier},
     volume = {59},
     year = {2009},
     pages = {2429-2444},
     doi = {10.5802/aif.2495},
     zbl = {1191.14060},
     mrnumber = {2640925},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2009__59_6_2429_0}
}

Fresse, Lucas. Singular components of Springer fibers in the two-column case. Annales de l'Institut Fourier, Tome 59 (2009) pp. 2429-2444. doi : 10.5802/aif.2495. http://gdmltest.u-ga.fr/item/AIF_2009__59_6_2429_0/

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