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Write S_{\\lambda} S_{\\mu} for the subspace of S spanned by products of S_{\\lambda} and S_{\\mu}. If V_{\\nu} occurs as an irreducible constituent of the tensor product of V_{\\lambda} and V_{\\mu}, is it true that S_{\\nu} is contained in S_{\\lambda} S_{\\mu}? 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Let S denote the ring of polynomials on V. Assume that the action of K on S is multiplicity free. If V_{\\lambda} is an irreducible representation of K, let S_{\\lambda} denote the corresponding isotypic component of S. Write S_{\\lambda} S_{\\mu} for the subspace of S spanned by products of S_{\\lambda} and S_{\\mu}. If V_{\\nu} occurs as an irreducible constituent of the tensor product of V_{\\lambda} and V_{\\mu}, is it true that S_{\\nu} is contained in S_{\\lambda} S_{\\mu}? 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