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.
Bartolone Claudio, Vaccaro Maria Alessandra (1999). The action of the symplectic group associated with a quadratic extension of fields. JOURNAL OF ALGEBRA, 220, 115-151 [10.1006/jabr.1999.7921].
The action of the symplectic group associated with a quadratic extension of fields
Bartolone Claudio;Vaccaro Maria Alessandra
1999-01-01
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.
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