Broer, Bram On the generating functions associated to a system of binary forms. (English) Zbl 0703.15031 Indag. Math., New Ser. 1, No. 1, 15-25 (1990). 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 Cited in 1 ReviewCited in 5 Documents MSC: 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 Keywords:generating functions; binary forms; ring of invariants; modules of covariants; Cohen-Macaulay type PDF BibTeX XML Cite \textit{B. Broer}, Indag. Math., New Ser. 1, No. 1, 15--25 (1990; Zbl 0703.15031) Full Text: DOI OpenURL References: [1] Almkvist, G., Some formulas in invariant theory, J. of alg., 77, 338-359, (1982) · Zbl 0492.20032 [2] Bergh, M.van den, Trace rings of generic matrices are Cohen-Macaulay, J. am. math. soc., 2, 775-800, (1989) · Zbl 0697.20025 [3] Brion, M., Invariants de plusieurs formes binaires, Bull. soc. fr., 110, 429-445, (1982) · Zbl 0508.14006 [4] Brouwer, A.E.; Cohen, A.M., The Poincaré series of the polynomials invariant under SU2 in its irreducible representation of degree <17, (), 134 [5] Dixmier, J., Quelques résultats et conjectures concernants des formes binaires, () · Zbl 0578.14011 [6] Franklin, F., On the calculation of the generating functions and tables of groundforms for binary quantics, Amer. J. math., 3, 128-153, (1880) · JFM 12.0086.02 [7] Springer, T.A., Invariant theory, () · Zbl 0346.20020 [8] Springer, T.A., On the invariant theory of SU2, Indag. math., 42, 339-345, (1980) · Zbl 0449.22017 [9] Stanley, R.P., Combinatorics and invariant theory, Proc. of symp. in pure math., Vol. 34, (1979) · Zbl 0411.22006 [10] Sylvester, J.J., Collected mathematical papers, vol. III, (1973), Chelsea This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.