A Clebsch-Gordan formula for SL_3 and applications to rationality

Details A Clebsch-Gordan formula for SL_3 and applications to rationality A Clebsch-Gordan formula for SL_3 and applications to rationality

2008-12-17

arxiv.org/abs/0812.3278v1

Advances in Mathematics Volume 224, Issue 1 (2010), 246-259

Mathematics

Algebraic Geometry

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

Scientific paper

10.1016/j.aim.2009.11.006

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.

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