On the singularity of the irreducible components of a Springer fiber in sl(n)

Abstract

Let ${\mathcal{B}}_u$ be the Springer fiber over a nilpotent endomorphism $u\in End({\mathbb{C}}^n)$. Let $J(u)$ be the Jordan form of $u$ regarded as a partition of $n$. The irreducible components of ${\mathcal{B}}_u$ are all of the same dimension. They are labelled by Young tableaux of shape $J(u)$. We study the question of singularity of the components of ${\mathcal{B}}_u$ and show that all the components of ${\mathcal{B}}_u$ are nonsingular if and only if $J(u)\in \{(\lambda ,1,1,...),({\lambda }_1,{\lambda }_2),({\lambda }_1,{\lambda }_2,1),(2,2,2)\}$.

19 pages

Cited by in corpus (7)

• 2-row Springer fibres and Khovanov diagram algebras for type D
• Springer fiber components in the two columns case for types A and D are normal
• Springer fibers and Schubert points
• Some characterizations of singular components of Springer fibers in the two-column case
• Exotic Springer fibers for orbits corresponding to one-row bipartitions
• Patch ideals and Peterson varieties
• Two-row Delta Springer varieties