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

TL;DR

This paper explores the structure of nilpotent orbits in affine Kac-Moody algebras, specifically providing a parameterization for the case of alculus sl_n^{(1)}(\u00a0C), advancing understanding of their classification.

Contribution

It introduces a new framework for defining nilpotent orbits in affine Kac-Moody algebras and offers a specific parameterization for alculus sl_n^{(1)}(C).

Findings

Defined nilpotent orbits in affine Kac-Moody algebras.

Provided a parameterization for alculus sl_n^{(1)}(C).

Enhanced classification methods for nilpotent orbits.

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