Am I entitled to a raise for a interim position?

Over a week ago, the assistant manager at our store put in his notice that he’d be taking a different job. Our store manager came up to me and told me I’d be taking the interim assistant manager position (I wasn’t even given a choice) and was also told I wouldn’t get a pay raise while in the interim position (assistant managers make a dollar more an hour plus bigger commission payouts) is this something they can actually do?