The real model orbit of type E8

Motivated by the so-called orbit method to construct unitary representations of a reductive Lie group, Adams Huang and Vogan studied the model orbit of the complex algebraic group E8, that is, the adjoint nilpotent orbit whose coordinate ring is the multiplicity-free direct sum of all the irreducible representations. They also studied a real analogue of it, an adjoint nilpotent orbit of the split real form of E8. Under the Kostant-Sekiguchi correspondence this is associated with an orbit of the complex algebraic group Spin(16), which we are able to study by making use of our results on the projective normality of wonderful varieties, and proving a couple of conjectures left open by Adams Huang and Vogan. This is a joint work with Jacopo Gandini and Andrea Maffei.