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comment Is there “Schur-Weyl duality” for infinite dimensional unitary group?
I should have also mentioned that the direct limit of the finite-dimensional groups is dense in $U(\mathcal{H})$.
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revised Is there “Schur-Weyl duality” for infinite dimensional unitary group?
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comment Is there “Schur-Weyl duality” for infinite dimensional unitary group?
I am not sure I understand your comment. Every representation of the infinite-dimensional unitary group restricts to a representation of the direct limit of finite-dimenssional unitary groups and conversely, each of the representations they consider extends to one of the full unitary group.
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answered Is there “Schur-Weyl duality” for infinite dimensional unitary group?
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comment What are some reasonable-sounding statements that are independent of ZFC?
Maybe I didn't choose the right word. Anyway, for me, PD is a strong justification for large cardinals, not the other way round. But this is, of course, a philosophical rather than mathematical discussion.
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answered What are some reasonable-sounding statements that are independent of ZFC?
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answered What are some reasonable-sounding statements that are independent of ZFC?