Singular components of Springer fibers in the two-column case
Annales de l'Institut Fourier, Volume 59 (2009) no. 6, p. 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 : https://doi.org/10.5802/aif.2495
Classification:  14M15,  14B05
Keywords: Flag varieties, Springer fibers, singularity criteria, Young tableaux
@article{AIF_2009__59_6_2429_0,
     author = {Fresse, Lucas},
     title = {Singular components of Springer fibers in the two-column case},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {6},
     year = {2009},
     pages = {2429-2444},
     doi = {10.5802/aif.2495},
     mrnumber = {2640925},
     zbl = {1191.14060},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_6_2429_0}
}
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://www.numdam.org/item/AIF_2009__59_6_2429_0/

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