Aarhus University Seal

HyperKähler Potentials via Finite-Dimensional Quotients

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


  • Piotr Kobak, Jagiellonian University in Kraków
  • ,
  • Andrew Swann

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, ℂ)-orbits of elements with X2 = 0, are in fact hyperKähler potentials.

Original languageEnglish
JournalGeometriae Dedicata
Pages (from-to)1-19
Number of pages19
Publication statusPublished - 1 Dec 2001
Externally publishedYes

    Research areas

  • Classical Lie algebras, HyperKähler manifold, HyperKähler potential, HyperKähler quotient, Nilpotent orbit

See relations at Aarhus University Citationformats

ID: 151850978