Rationality of adjoint orbits

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 homogeneous affine Hamiltonian $G$-varieties (which we classify).

Keywords

orbit of linear algebraic group, rational algebraic variety, Hamiltonian variety

2010 Mathematics Subject Classification

Primary 14E08, 14M20. Secondary 14L24, 14L30.

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Received 9 November 2022

Accepted 11 February 2023

Published 26 March 2024