On the generating functions associated to a system of binary forms. (English) Zbl 0703.15031

A class of generating functions associated with a system of m-binary forms is derived as solutions of some explicit systems of inhomogeneous linear equations with coefficients in the field of rational functions in m variables. Thus by using this class of generating functions, the ring of invariants and some modules of covariants can be written as the quotient of the determinant of two explicit matrices. This has some implications for the Cohen-Macaulay type of modules of covariants over the ring of invariants.
Reviewer: J.K.Sengupta


15A72 Vector and tensor algebra, theory of invariants
15B33 Matrices over special rings (quaternions, finite fields, etc.)
13A50 Actions of groups on commutative rings; invariant theory
16D80 Other classes of modules and ideals in associative algebras
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