Geometriae Dedicata

, Volume 34, Issue 3, pp 281–293

Field extensions and isotropic subspaces in symplectic geometry

  • Dae San Kim
  • Patrick Rabau

DOI: 10.1007/BF00181690

Cite this article as:
Kim, D.S. & Rabau, P. Geom Dedicata (1990) 34: 281. doi:10.1007/BF00181690


Let L/k be a finite field extension and let (V, B) be a finite dimensional symplectic space over L. We examine the action of the symplectic group SpL(V) on the set of B′-isotropic k-subspaces of V, where B′=ψ°B is the k-symplectic form induced by a ‘trace’ map ψ:Lk. The orbits are completely classified in the case of a quadratic extension and for maximal B′-isotropic subspaces in the case of a cubic extension; the number of orbits of maximal B′-isotropic subspaces is shown to be infinite if the degree of the extension is at least 4.

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Dae San Kim
    • 1
  • Patrick Rabau
    • 2
  1. 1.Department of MathematicsSeoul Woman's UniversitySeoulKorea
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusUSA

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