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The Molien function associated with a finite-dimensional representation of a compact Lie group is a useful tool in representation theory because it acts as a generating function for counting the number of invariant polynomials on the representation space. The main purpose of this paper is to introduce a more general ͑and apparently new͒ generating function which, in the same sense, counts not only the number of invariant real polynomials in a real representation or the number of invariantdoi:10.1063/1.532373 fatcat:bpbe5ftukbf3teew6o7zygs2cm