ABOUT GORDAN'S ALGORITHM FOR BINARY FORMS

Marc Olive (1)

1 I2M - Institut de Mathématiques de Marseille

In this paper, we present a modern version of Gordan's algorithm on binary forms. Symbolic method is reinterpreted in terms of SL(2, C)–equivariant homomorphisms defined upon Cayley operator and polarization operator. A graphical approach is thus developed to obtain Gordan's ideal, a central key to get covariant basis of binary forms. To illustrate the power of this method, we obtain for the first time a minimal covariant bases for S6 ⊕ S4, S6 ⊕ S4 ⊕ S2 and a minimal invariant bases of S8 ⊕ S4 ⊕ S4.

Mots clés: Classical invariant theory; Covariants; Algorithm

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Marc Olive. ABOUT GORDAN'S ALGORITHM FOR BINARY FORMS. 2014. ⟨hal-00952988v4⟩