Normality of very even nilpotent varieties in D_2l

Abstract

For the classical groups, Kraft and Procesi have resolved the question of which nilpotent orbits have closures which are normal and which are not, with the exception of the very even orbits in $D_{2l}$ which have partition of the form $(a^{2k},b^2)$ for $a,b$ distinct even natural numbers with $ak+b=2l$. In this article, we show that these orbits do have normal closure.