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

Prove that the uniform, purely unitary easy groups are

[[math]] \xymatrix@R=50pt@C=50pt{ C_N\ar[r]&U_N\\ S_N\ar[u]\ar[r]&K_N\ar[u]} [[/math]]

with a suitable definition for the notion of pure unitarity.