A Clebsch-Gordan formula for SL_3 and applications to rationality

Abstract

If R, S, T are irreducible SL_3-representations, we give an easy and explicit description of a basis of the space of equivariant maps from R tensor S to T. 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.

16 pages; 1 figure; Macaulay2 scripts used can be found at http://www.uni-math.gwdg.de/bothmer/ClebschGordan/ or at the end of the latex source file