The action of the symplectic group associated with a quadratic extension of fields

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Abstract

Given a quadratic extension L/K of fields and a regular alternating space (V; f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group Sp_L(V; f) in the set of K-subspaces of V.
Original languageEnglish
Pages (from-to)115-151
Number of pages37
JournalJournal of Algebra
Volume220
Publication statusPublished - 1999

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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