There are two impediments here:
Purely mental actions
“Purely mental action” is not a strictly-defined term in the rules, so we are left trying to categorize actions as this based on our real-world understanding of the terms. The sense of the term is that any action that requires some kind of physical movement (of the person, of the hands, of an object, etc. etc.) is not purely mental, and all other actions are.
No physical movement is obviously associated with concentrating, and while the Concentration skill notes several types of forced movement that make concentrating harder, it makes no mention of paralysis preventing concentration. The paralysis condition itself also uses the term “purely mental actions” to describe what a paralyzed creature can do.
Finally, the FAQ, flawed though it is, does cover the question of purely mental actions on page 94, and explicitly lists concentration as one of the actions that is purely mental:
What exactly counts as a “purely mental” action, such as those allowed to the second mind created by the schism power (XPH 130)?
- Concentrating to maintain a spell.
So based on these pieces of evidence, while none of it comes out and explicitly and authoritatively states that concentration is a purely mental action, it seems to be a very safe claim to say it is.
Manifesting while concentrating on another power
You can’t manifest a power while concentrating on another one.
This is not a problem. You aren’t concentrating on the power. The schism-created-copy-of-you is concentrating. Thus you are still free to manifest another power. This is consistent with something schism does explicitly state:
Your second mind doesn’t provoke attacks of opportunity when manifesting a power, because doing so doesn’t distract your primary mind.
Just like how the schism-created-copy-of-you does not distract you when manifesting, its concentration also does not prevent you from focusing on manifesting another power, since it is not requiring your attention.
A snag here: transferring concentration?
One issue that is not well-addressed is the question of whether or not the schism-created-copy-of-you can concentrate on a power that you manifested in the first place. That is, can you transfer the responsibility of concentrating on a power to the schism-created-copy-of-you?
If not, then the schsim-created-copy-of-you can only concentrate on powers that it manifested in the first place, which means only powers manifested under that −6 penalty to manifester level (and, more importantly, maximum power points spent). And if you manifest a power requiring concentration, and you can’t transfer that, then you are left manifesting only with the schism-created-copy-of-you, again with that −6 penalty to manifester level.
I would argue that you cannot perform this kind of transfer to the schism-created-copy-of-you. This kind of transfer is possible, but you need a special power to do it—like solicit psicrystal, which transfers concentrating to your psicrystal. The schism power does not give you any such explicit ability to transfer concentration, so you cannot.