Is it permissible for a legal agent for sale to stipulate to the broker that they split the commission equally, and what are the conditions for that?

The agent is only allowed what he has been authorized to do. The agent's condition of taking half of the commission for himself without the permission of his principals is impermissible and considered deceit and fraud. This is because it might motivate him not to thoroughly pursue the best price and profit in order to secure the commission. The agent does not have the authority to act beyond what is entailed by his principal's permission.