On the invariant theory of the Bezoutiant

الأصل · EN

We study the classical invariant theory of the Bezoutiant R(A,B) of a pair of binary forms A,B. It is shown that R(A,B) admits a Taylor expansion whose coefficients are (essentially) the odd transvectants (A,B)₂ᵣ₊₁. Moreover, R(A,B) is entirely determined by the first two terms M = (A,B)₁, N =(A,B)₃. Using the Plucker relations, we give equivariant formulae which express the higher transvectants (A,B)₅, (A,B)₇ in terms of M,N. We also describe a `reduction formula' which calculates B from the knowledge of A and R(A,B).