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

Nicolas Perrin; Evgeny Smirnov — 2012

Bulletin de la Société Mathématique de France

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.

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