2000/01/05 by Piotr Kobak, Andrew Swann, Kobak, Piotr +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.math/0001027
20 pages, LaTeX with AMS macros
arxiv created 2000/01/05 · openalex publication_date 2000/01/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that nilpotent orbits in a complex simple Lie algebra admit hyperKähler metrics with a single function that is a global potential for each of the Kähler structures (a hyperKähler potential). In an earlier paper the authors showed that nilpotent orbits in classical Lie algebras can be constructed as finite-dimensional hyperKähler quotient of a flat vector space. This paper uses that quotient construction to compute hyperKähler potentials explicitly for orbits of elements with small Jordan blocks. It is seen that the Kähler potentials of Biquard and Gauduchon for SL(n)-orbits of elements with X2=0, are in fact hyperKähler potentials.