Nilpotent orbits of Kac-Moody algebras and its parameterization for $\mathfrak{sl}_n^{(1)}(\mathbb C)$

Abstract

In the context of affine complex Kac-Moody algebras, we define the meaning of nilpotent orbits under the adjoint action of the maximal Kac-Moody group. We also give a parameterization of nilpotent orbits of $\mathfrak{sl}_n^{(1)}(\mathbb C)$.