Lie Group Representations on Polynomial Rings
نویسندگان
چکیده
0. Introduction. 1. 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 5 be the ring of all complexvalued polynomials on X, regarded as a G-module in the obvious way, and let J C 5 be the subring of all G-invariant polynomials on X. Now let J be the set of all ƒ £ J having zero constant term and let HQS be any graded subspace such that S=JS+H is a G-module direct sum. I t is then easy to see that
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