How does singlet oxygen work in pericyclics?

[CrimpJiggler]

and here's the diagram for the ^1O₂ dienophile:

Its the ¹E⁺_g the one I'm interested in. I see that its single electrons are in a couple of degenerate pi orbitals. I'm having trouble figuring out what the LUMO is here. Does it even matter that I have 2 LUMOs? I kinda suspect, that would make it much more reactive since unpaired electrons are pretty unstable. Is this oxygen singlet species technically a diradical?

 

[DrDu]

The MO diagram for singlet oxygen from wikipedia is not quite correct insofar as it is not a pi_x or pi_y orbital which is doubly occupied in singlet oxygen but rather a $\pi^*_\pm=\frac{1}{\sqrt{2}}(\pi^*_x\pm i\pi^*_y)$ orbital.
So let's say that the $\pi^*_+$ is doubly occupied, then the $\pi^*_-$ is the LUMO.