Can you hook up Canon speedlight to a wall outlet?

No, but you can find a used or generic replacement for the Canon CP-E4, which holds 8 AA cells (roughly doubling the 580EXII's battery life and increases its recycle times.

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Insanity is defined as doing the same thing repeatedly and expecting a differrent result. Taking the same shot, w/the same exposure and expecting greatness- Hasn't happened for ME, yet... How about you?