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

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over; Pr; ON THE SYMPLECTIC INVARIANTS OF A SUBSPACE OF A VECTOR SPACE;
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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(F)={T: 2v×2v matrix over F|TKT~T=K}. It is well-known that Sp(F) is a group with respect to the matrix multiplication and is called the symplectic group of degree 2v over F
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