Rationality of adjoint orbits

TL;DR

This paper proves that all adjoint orbits of connected reductive algebraic groups are rational varieties, and classifies rational affine Hamiltonian G-varieties for complex simply connected semisimple groups.

Contribution

It establishes the rationality of all adjoint orbits for connected reductive groups and classifies rational affine Hamiltonian G-varieties for certain complex groups.

Findings

All adjoint orbits are rational algebraic varieties.

Classification of rational affine Hamiltonian G-varieties for complex simply connected semisimple groups.

Implication for the structure of algebraic group actions.

Abstract

We prove that every orbit of the adjoint representation of any connected reductive algebraic group $G$ is a rational algebraic variety. For complex simply connected semisimple $G$, this implies rationality of affine Hamiltonian $G$-varieties (which we classify).