We describe the branching rule from to , where the latter is embedded via its action on binary cubic forms. We obtain both a numerical multiplicity formula, as well as a minimal system of generators for the geometric realization of the rule.
Let k be a field and k[x,y] the polynomial ring in two variables over k. Let D be a higher k-derivation on k[x,y] and D̅ the extension of D on k(x,y). We prove that if the kernel of D is not equal to k, then the kernel of D̅ is equal to the quotient field of the kernel of D.
On décrit l’algèbre des invariants de l’action naturelle du groupe sur les pinceaux de formes quintiques binaires.