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 ${\mathfrak{sl}}_n^{(1)}(\mathbb{C})$.