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Lie Group Representations On Polynomial Rings

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Abstract

Let G be a group of linear transformations on a finite dimensional real or complex vector space X. Assume X is completely reducible as a G-module. Let S be the ring of all complex-valued polynomials on X, regarded as a G-module in the obvious way, and let J ? S be the subring of all G-invariant polynomials on X.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

    Bertram Kostant

Authors
  1. Bertram Kostant
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Correspondence to Bertram Kostant .

Editor information

Editors and Affiliations

  1. Fac. Mathematics & Computer Science, Weizmann Institute of Science, Rehovot, 76100, Israel

    Anthony Joseph

  2. Dept. Mathematics, University of North Carolina, Phillips Hall, Chapel Hill, 27599-3250, U.S.A.

    Shrawan Kumar

  3. Centre de Mathématiques, Ecole Polytechnique, Palaiseau Cedex, 91128, France

    Michèle Vergne

Additional information

Communicated by Raoul Bott, February 1, 1963

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© 2009 Springer-Verlag New York

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Kostant, B. (2009). Lie Group Representations On Polynomial Rings. In: Joseph, A., Kumar, S., Vergne, M. (eds) Collected Papers. Springer, New York, NY. https://doi.org/10.1007/b94535_16

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