# 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}
}
• Published 1 December 1990
• Mathematics
• Inventiones mathematicae
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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• Mathematics
• 2014
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Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-
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: We consider the generalized doubling integrals of Cai, Friedberg, Ginzburg and Kaplan. These generalize the doubling method of Piatetski-Shapiro and Rallis and represent the standard L-function for