Composantes singulières des fibres de Springer dans le cas deux-colonnes

Fresse, Lucas

doi:10.1016/j.crma.2009.04.005

Géométrie algébrique

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

Presented by: Michel Duflo

Fresse, Lucas ¹

¹ Department of Mathematics, the Weizmann Institute of Science, 76100 Rehovot, Israel

Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 631-636.

Abstract
Résumé

We consider the Springer fiber $B_{u}$ corresponding to a nilpotent endomorphism u of nilpotent order 2. We establish a necessary and sufficient condition of singularity for the components of $B_{u}$ .

On considère la fibre de Springer $B_{u}$ pour un endomorphisme nilpotent u tel que $u^{2} = 0$ . On établit une condition nécessaire et suffisante de singularité pour les composantes de $B_{u}$ .

Received: 2008-11-09
Accepted: 2009-04-02
Published online: 2009-04-23

DOI: 10.1016/j.crma.2009.04.005

Author's affiliations:

Fresse, Lucas ¹

¹ Department of Mathematics, the Weizmann Institute of Science, 76100 Rehovot, Israel

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     title = {Composantes singuli\`eres des fibres de {Springer} dans le cas deux-colonnes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {631--636},
     publisher = {Elsevier},
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Fresse, Lucas. Composantes singulières des fibres de Springer dans le cas deux-colonnes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 631-636. doi : 10.1016/j.crma.2009.04.005. http://www.numdam.org/articles/10.1016/j.crma.2009.04.005/

References
Cited by

[1] Fung, F.Y.C. On the topology of components of some Springer fibers and their relation to Kazhdan–Lusztig theory, Adv. Math., Volume 178 (2003), pp. 244-276

[2] Spaltenstein, N. Classes unipotentes et sous-groupes de Borel, Lecture Notes in Math., vol. 946, Springer-Verlag, Berlin, New York, 1982

[3] Springer, T.A. The unipotent variety of a semisimple group, Proc. Colloq. Alg. Geom. Tata Institute, Oxford Univ. Press, London, 1969, pp. 373-391

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