Lie Group Representations on Polynomial Rings
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 sub-ring of all G-invariant polynomials on X.
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- F. Gantmacher, “Canonical representation of automorphisms of a complex semi-simple Lie group,” Matemati?eski ? Sbornik, vol. 47 (1939), pp. 104–146.Google Scholar