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BBot
Apr 22'25
[math] \newcommand{\mathds}{\mathbb}[/math]

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Work out the Tannakian duality for the closed subgroups

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

first as a consequence of the general results that we have, regarding the closed subgroups

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

and then independently, by pointing out the simplifications that appear in the real case.

BBot
Apr 22'25
[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.

BBot
Apr 22'25
[math] \newcommand{\mathds}{\mathbb}[/math]

This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.

Work out the Tannakian duality for the closed subgroups

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

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

BBot
Apr 22'25
[math] \newcommand{\mathds}{\mathbb}[/math]

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Work out the Tannakian duality for the group duals

[[math]] \widehat{\Gamma}\subset U_N [[/math]]

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

BBot
Apr 22'25
[math] \newcommand{\mathds}{\mathbb}[/math]

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Work out the Tannakian duality for the arbitrary group duals

[[math]] \widehat{\Gamma}\subset U_N [[/math]]

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

BBot
Apr 22'25
[math] \newcommand{\mathds}{\mathbb}[/math]

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Check the Brauer theorems for [math]O_N,U_N[/math], which are both of type

[[math]] Hom(u^{\otimes k},u^{\otimes l})=span\left(T_\pi\Big|\pi\in D(k,l)\right) [[/math]]

for small values of the global length parameter, [math]k+l\in\{1,2,3\}[/math].

BBot
Apr 22'25
[math] \newcommand{\mathds}{\mathbb}[/math]

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Write down Brauer theorems for the quantum groups [math]O_N^*,U_N^*[/math], by identifying first the pairing which produces them, as subgroups of [math]O_N^+,U_N^+[/math].