[math] \newcommand{\mathds}{\mathbb}[/math]

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Work out the Tannakian duality for the closed subgroups

[[math]] G\subset U_N^+ [[/math]]

whose fundamental corepresentation is self-adjoint, up to equivalence,

[[math]] u\sim\bar{u} [[/math]]

first as a consequence of the results that we have, and then independently.