SPRINGER FIBER COMPONENTS IN THE TWO COLUMNS CASE FOR TYPES A AND D ARE NORMAL

摘要

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.