Determining representations from invariant dimensions

@article{Larsen1990DeterminingRF,
  title={Determining representations from invariant dimensions},
  author={Michael Larsen and Richard Pink},
  journal={Inventiones mathematicae},
  year={1990},
  volume={102},
  pages={377-398}
}
This paper is motivated by the following "Tannakian" question: to what extent is a complex Lie group, G, and a finite dimensional representation, (p, V) of G, determined by the dimensions of the various invariant spaces W G, where the W are obtained from V by linear algebra? That is, given dim((Sym2(V)a), dim((A 3 V)~), etc., can one determine (G, p)? This problem arises, for instance, in the cohomological study of exponential sums; we intend to apply the below results to the problem of… 

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