Pure and Applied Mathematics Quarterly

Volume 20 (2024)

Number 1

Special Issue dedicated to Corrado De Concini

Guest Editors: Alberto De Sole, Nicoletta Cantarini, and Andrea Maffei

Rationality of adjoint orbits

Pages: 525 – 535

DOI: https://dx.doi.org/10.4310/PAMQ.2024.v20.n1.a11

Author

Vladimir L. Popov (Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia)

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 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.

Received 9 November 2022

Accepted 11 February 2023

Published 26 March 2024