Air Canada has like 1 year in operation between Canada and PUJ, now they operate flights to POP. These operations are results of merge with some other canadian carriers that used to operate from Canada to Dominicana.
Air Canada's flights to Dominicana are served on charter basis, no regular sales are allowed, flights are not listed in reservation systems nor on their website. Only authorized canadian travel agents are allowed to sell tickets. Prices are subjects of travel status, inclusive tour fares are low, but Air Transat is still cheaper.
It is the same story as we have with Air Transat, they fly but don't sell here, ticketing is allowed only on their own stocks.
Today I've seen AC here in POP.