We consider the Springer fiber corresponding to a nilpotent endomorphism of nilpotent order . As a first result, we give a description of the elements of a given component of which are fixed by the action of the standard torus relative to some Jordan basis of . By using this result, we establish a necessary and sufficient condition of singularity for the components of .
On considère la fibre de Springer pour un endomorphisme nilpotent tel que . On décrit les éléments des composantes de qui sont fixés par l’action du tore standard relatif à une base de Jordan de . À l’aide de ce résultat, on établit une condition nécessaire et suffisante de singularité pour les composantes de .
Keywords: Flag varieties, Springer fibers, singularity criteria, Young tableaux
Mot clés : variétés de drapeaux, fibres de Springer, critères de singularité, tableaux de Young
@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}, 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}, mrnumber = {2640925}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2495/} }
TY - JOUR AU - Fresse, Lucas TI - Singular components of Springer fibers in the two-column case JO - Annales de l'Institut Fourier PY - 2009 SP - 2429 EP - 2444 VL - 59 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2495/ DO - 10.5802/aif.2495 LA - en ID - AIF_2009__59_6_2429_0 ER -
%0 Journal Article %A Fresse, Lucas %T Singular components of Springer fibers in the two-column case %J Annales de l'Institut Fourier %D 2009 %P 2429-2444 %V 59 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2495/ %R 10.5802/aif.2495 %G en %F 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://archive.numdam.org/articles/10.5802/aif.2495/
[1] On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory, Adv. Math. (2003) no. 178, pp. 244-276 | DOI | MR | Zbl
[2] Description of -orbit closures of order 2 in upper triangular matrices, Transf. Groups (2006) no. 11, pp. 217-247 | DOI | MR
[3] Reducibility of the intersections of components of a Springer fiber (to appear in Indag. Math.)
[4] Four lectures on simple groups and singularities, Communications of the Mathematical Institute, Volume 11, Rijksuniversiteit Utrecht, 1980 | MR | Zbl
[5] Classes unipotentes et sous-groupes de Borel, Lecture Notes in Mathematics, Volume 946, Springer-Verlag, Berlin-New York, 1982 | MR | Zbl
[6] Fixed points under the action of unipotent elements of in the flag variety, Bol. Soc. Mat. Mexicana (1979) no. 24, pp. 1-14 | MR | Zbl
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