A characterization of nilpotent orbit closures among symplectic   singularities
  We prove that a conical symplectic variety with maximal weight 1 is isomorphic to one of the following:   (i) an affine space with the standard symplectic form   (ii) a nilpotent orbit closure of a complex semisimple Lie algebra with the Kirillov-Kostant form. 
Yoshinori Namikawa
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