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I am wondering whether the Rallis inner product on unitary group is finished.

Espescially, I am considering two cases, that is, both ( U(2) -> U(1) ) case & (U(1) -> U(1) ) case.

Are these cases already over? If it is, would you recommend me what paper should I refer?

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Please read 'how to ask'. – quid Dec 9 at 0:59

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