Singular components of the Springer fiber in the two-columns case

Abstract

We consider the Springer fiber ${\mathcal{B}}_u$ 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 ${\mathcal{B}}_u$ 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 ${\mathcal{B}}_u$.

arXiv comment11 pages

Cited by in corpus (2)

• Springer fiber components in the two columns case for types A and D are normal
• Some characterizations of singular components of Springer fibers in the two-column case