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Индекс 1-формы на вещественной фактор-особенности

Let G be a finite Abelian group acting (linearly) on space ℝn and, therefore, on its complexification ℂn, and let W be the real part of the quotient ℂn/G (in the general case, W ≠ ℝn/G). The index of an analytic 1-form on the space W is expressed in terms of the signature of the residue bilinear form on the G-invariant part of the quotient of the space of germs of n-forms on (ℝn, 0) by the subspace of forms divisible by the 1-form under consideration.