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Singular components of Springer fibers in the two-column case

Lucas Fresse — 2009

Annales de l’institut Fourier

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 .

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