Are the brothers entitled to demand partnership in commercial shops that their brother established with his own effort and money, financed by a loan from their deceased father's shops, given that he has repaid a large portion of this loan?

Since the agency is nullified by the death of the principal, your father's authorization to you was nullified by his death. Your management of the shops by opening them in your name and financing them from the original shops without the permission of the other heirs is considered an infringement upon their right. Therefore, you must return everything you took in full, and the profit is yours alone. The shops you opened in your name are yours, and you must return what is measurable with its like and what is appraisable with its value, and divide the inheritance to give every rightful person his due.