
Journal of Lie Theory 21 (2011), No. 1, 205242 Copyright Heldermann Verlag 2011 On the Singularity of some Special Components of Springer Fibers Lucas Fresse Department of Mathematics, Weizmann Institute of Science, 76100 Rehovot, Israel lucas.fresse@weizmann.ac.il Let V be an ndimensional Cvector space and let u from V to V be a nilpotent endomorphism. The variety of ustable complete flags is called the Springer fiber over u. Its irreducible components are parameterized by a set of standard Young tableaux. The Richardson (respectively, BalaCarter) components of Springer fibers correspond to the Richardson (resp. BalaCarter) elements of the symmetric group, through RobinsonSchensted correspondence. Every Richardson component is isomorphic to a product of standard flag varieties. By contrast, the BalaCarter components are very susceptible to be singular. First, we characterize the singular BalaCarter components in terms of two minimal forbidden configurations. Next, we introduce two new families of components, wider than the families of BalaCarter 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. Keywords: Springer fibers, Richardson components, BalaCarter components, singularity criteria, iterated bundles. MSC: 14M15; 05E10, 20G05 [ Fulltextpdf (383 KB)] for subscribers only. 