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

Given a closed subgroup [math]G\subset_uU_N[/math], understand and then briefly explain, in a short piece of writing, why the [math]*[/math]-algebras

[[math]] C(k,k)=End(u^{\otimes k}) [[/math]]

form a planar algebra in the sense of Jones, and then comment as well on the various formulations of Tannakian duality, in the planar algebra setting.