to achieve this behaviour - user will be able to manage only products from specified department - follow these steps:
- assign the user to role, e.g. Department1ManagerRole. See the Configurating permission section in Kentico documentation,
- grant the Read products and Modify products permissions to the role user is assigned to (Department1ManagerRole). See the E-commerce permission section in Kentico documentation),
- go to Users application -> edit your user -> go to tab Departments -> assign the department (Department1) to the user
Now you have the user (in role Department1ManagerRole) who is able to manage the products only from department Department1.
You can also follow step by step scenario in E-commerce department managers section in Kentico documentation. Hope it will help you.