A Clebsch–Gordan formula for [formula omitted] and applications to rationality

Abstract

If R, S, T are irreducible SL 3 ( C ) -representations, we give an easy and explicit description of a basis of the space of equivariant maps R ⊗ S → T (Theorem 3.1). We apply this method to the rationality problem for invariant function fields. In particular, we prove the rationality of the moduli space of plane curves of degree 34. This uses a criterion which ensures the stable rationality of some quotients of Grassmannians by an SL-action (Proposition 5.4).