Classical Invariant Theory

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 301)


In the comparison of the homology of the Lie algebra of matrices with cyclic homology one of the key points is the following result which pertains to invariant theory: there is an isomorphism
$$ {(gl{\left( k \right)^{ \otimes n}})_{gl(k)}} \cong k\left[ {{S_n}} \right] $$


Invariant Theory Young Diagram Fundamental Theorem Young Tableau Symplectic Group 
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Bibliographical Comments on Chapter 9

  1. Weyl, H., The classical groups, Princeton University Press, 1946.Google Scholar
  2. Procesi, C., The invariant theory of nxn-matrices, Adv. in Math. 19 (1976), 306–381.MathSciNetzbMATHGoogle Scholar
  3. Procesi, C., Trace identities and standard diagrams, in Ring theory, Proc. Antw. Conf. 1978, Dekker (1979), 191–218.Google Scholar
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  5. Kostant, B., A theorem of Frobenius, a theorem of Amitsur-Levitzki and cohomology theory, J. Math. Mech. 7 (1958), 237–264.MathSciNetzbMATHGoogle Scholar
  6. Atiyah, M.F., Tall, D.O., Group representations, A-rings and the J-homomorphism, Topology 8 (1969), 253–297.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Fiedorowicz, Z., Ogle, C., Vogt, Volodin K-theory of Aring spaces, preprint. Formanek, E., The polynomial identities and invariant nxn-matrices, Cbms Lect. Note 78, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeCentre National de la Recherche ScientifiqueStrasbourgFrance

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