Field extensions and isotropic subspaces in symplectic geometry

✍ Scribed by Dae San Kim; Patrick Rabau

• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 571 KB
• Volume: 34
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00181690

✦ Synopsis

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 ksubspaces of V, where B' = ~p o B is the k-symplectic form induced by a 'trace' map tp: L --, k. 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.