Nilpotent orbits of sl(n,R) admit no Gibbs state
Jérémie Pierard de Maujouy, Guillaume Neuttiens
Abstract
Gibbs states are probability distributions defined on Hamiltonian G-manifolds. They are parametrized by an open set of the Lie algebra g and arise as natural equilibrium states with regard to the action of G on the system. In this paper, we focus on nilpotent orbits of SL(n,R). We show that for n>2, those orbits do not admit any Gibbs state.
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