About Gordan's algorithm for binary forms

2014/03/04 by Marc Olive, Olive, Marc
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #math.AC #math.RT

paper · pdf · doi:10.48550/arxiv.1403.2283

arxiv created 2015/06/19 · arxiv updated 2015/06/22

Abstract

In this paper, we present a modern version of Gordan's algorithm on binary forms. Symbolic method is reinterpreted in terms of SL₂(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 bases of binary forms. To illustrate the power of this method, we obtain for the first time a minimal covariant basis for \Sn6⊕\Sn4 and \Sn6⊕\Sn4⊕ \Sn2.

Related

• Brill-Gordan Loci, Transvectants and an Analogue of the Foulkes Conjecture
• Covariant algebra of the binary nonic and the binary decimic
• Reduction theory of binary forms
• Binary forms with covariant points close to the real axis
• Semi-invariants of Binary Forms and Sylvester's Theorem