Geodesic
On the Singularity of some Special Components of Springer Fibers
Lucas Fresse1
1Department of Mathematics, Weizmann Institute of Science, 76100 Rehovot, Israel
Journal of Lie Theory, Tome 21 (2011) no. 1, pp. 205-242

Voir la notice de l'article provenant de la source Heldermann Verlag

Let V be an n-dimensional C-vector space and let u from V to V be a nilpotent endomorphism. The variety of u-stable complete flags is called the Springer fiber over u. Its irreducible components are parameterized by a set of standard Young tableaux. The Richardson (respectively, Bala-Carter) components of Springer fibers correspond to the Richardson (resp. Bala-Carter) elements of the symmetric group, through Robinson-Schensted correspondence. Every Richardson component is isomorphic to a product of standard flag varieties. By contrast, the Bala-Carter components are very susceptible to be singular. First, we characterize the singular Bala-Carter components in terms of two minimal forbidden configurations. Next, we introduce two new families of components, wider than the families of Bala-Carter components and Richardson components, and both in duality via the tableau transposition. The components in the first family are characterized by the fact that they have a dense orbit of special type under the action of the stabilizer of u, whereas all components in the second family are iterated fiber bundles over projective spaces.
Classification : 14M15, 05E10, 20G05
Mots-clés : Springer fibers, Richardson components, Bala-Carter components, singularity criteria, iterated bundles

Lucas Fresse  1

1 Department of Mathematics, Weizmann Institute of Science, 76100 Rehovot, Israel 
Lucas Fresse. On the Singularity of some Special Components of Springer Fibers. Journal of Lie Theory, Tome 21 (2011) no. 1, pp. 205-242. http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a9/
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