I have a question regarding the map K[S_n] –> End(V^n). I think its an embedding. But Etingof states (Schur Weyl duality) that some of the representations L_lambda may be (0). On the other hand the double centralizer theorem says that this can not happen. Do you see my mistake?

Thank you

]]>Given that the group algebra of Sn is a semi-simple algebra, how do we know that the image of the group algebra in End E is also semi-simple? ( So we can use the double centralizer theorem )

Thank you

]]>Yes, I do need an identity theorem, and I’m proving it. The point is that by Lagrange interpolation, I only need to show that two polynomials of degree agree at points to show that they agree identically (the usual argument by factorization has to be applied to each component of these polynomials separately because they are really vector-valued polynomial functions, but the Lagrange interpolation argument applies without a need to break into components).

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