ON THE SYMPLECTIC INVARIANTS OF A SUBSPACE OF A VECTOR SPACE~*

Let F be any commutative field. Let v be an integer≥1 and be a fixed 2v × 2v nonsingular alternate matrix over F. Define Sp_(zv)(F)={T: 2v×2v matrix over F|TKT~T=K}. It is well-known that Sp_(2v)(F) is a group with respect to the matrix multiplication and is called the symplectic group of degree 2v over F