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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 $a k + b = 2 l$. In this article, we show that these orbits do have normal closure.
We determine which nilpotent orbits in $E_6$ have normal closure and which do not. We also verify a conjecture about small representations in rings of functions on nilpotent orbit covers for type $E_6$.
Let $mathcal{O}$ be a Richardson nilpotent orbit in a simple Lie algebra $mathfrak{g}$ over $mathbb C$, induced from a Levi subalgebra whose simple roots are orthogonal short roots. The main result of the paper is a description of a minimal set of ge
According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity of the nil
Every conic symplectic singularity admits a universal Poisson deformation and a universal filtered quantization, thanks to the work of Losev and Namikawa. We begin this paper by showing that every such variety admits a universal equivariant Poisson d
We study in this paper the jet schemes of the closure of nilpotent orbits in a finite-dimensional complex reductive Lie algebra. For the nilpotent cone, which is the closure of the regular nilpotent orbit, all the jet schemes are irreducible. This wa