The degree of covariant algebra two binary forms.
Keywords:
invariants, covariants, Poincaré series, binary formsAbstract
Using an explicit formula for the Poincare series for the algebra Сd1,d2, of covariants of two binary forms, we calculate the degree of this algebra for different cases of parity of numbers d1,d2.References
Benson D. Polynomial invariants of finite groups / D. Benson. – London Mathematical Society Lecture Note Series. 190: Cambridge University Press, 1993 – 118p.
Hilbert D. Ueber die vollen Invariantensysteme/ D. Hilbert // Math. Ann. – 1893. – V.42. – P. 313-373.
Springer T. Invariant theory / T. Springer. –Berlin: Springer-Verlag, 1977. – 111p.
Springer T.A. On the invariant theory of SU 2 //T.A.Springer// Indag.Math. – 1980. – V.42. – P. 339-345.
Bedratyuk L. The degree of the algebra of covariants of a binary forms / L.Bedratyuk, N. Ilash // Journal of Commutative Algebra. – 2015.–V. 7. – P.459-472.
Ilash N. The Poincaré series for the algebras of joint invariants and covariants of n linear forms / N. Ilash // C. R. Acad. Bulg. Sci. – 2015. – V. 68. – P. 715-724.
Bedratyuk L. The Poincaré series of the algebras of simultaneous invariants and covariants of two binary forms / L. Bedratyuk // Linear and Multilinear Algebra. – 2010. – V.58.– P.789-803.