Springer fiber components in the two columns case for types A and D are normal

Abstract

We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N^2=0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen-Macaulay, and have rational singularities.

v1: 18 pages; v2: 20 pages, Sec.3 rewritten, mistake in Prop.3.10 corrected

References in corpus (2)

• On the singularity of the irreducible components of a Springer fiber in sl(n)
• On frobenius splitting of orbit closures of spherical subgroups in flag varieties

Cited by in corpus (3)

• Some characterizations of singular components of Springer fibers in the two-column case
• On singularities in B-orbit closures of 2-nilpotent matrices
• Patch ideals and Peterson varieties