Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 397418 (2006) 

On the Invariant Theory of the B{é}zoutiantJaydeep V. Chipalkatti433 Machray Hall, Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Canada; email: jaydeep@cc.umanitoba.caAbstract: We study the classical invariant theory of the B{é}zoutiant ${\mathcal R}(A,B)$ of a pair of binary forms $A,B$. It is shown that ${\mathval R}(A,B)$ admits a Taylor expansion whose coefficients are (essentially) the odd transvectants $(A,B)_{2r+1}$; moreover ${\mathcal R}(A,B)$ is entirely determined by the first two terms $M = (A,B)_1, N =(A,B)_3$. Using the Pl{ü}cker 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 `generic reduction formula' which recovers $B$ from ${\mathcal R}(A,B)$ and $A$. Keywords: binary forms, B{é}zoutiant, transvectant, covariant, Grassmannian Classification (MSC2000): 13A50 Full text of the article:
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