The only significant diamond mine in the Western Hemisphere has opened in northern Canada. It will be producing 3.5 million to 4 million carats of quality gems annually when it goes fully online in 1999. Built in 17 months at a cost of about $700 million by BHP Diamonds, the Ekati mine lies in the frozen wastes of Canada’s Northwest Territories. The nearest city, Yellowknife, is 300 miles to the south; the Arctic Circle is 120 miles to the north. Ekati, pronounced “EK a tee,” is Inuit for “fat lake” (the mine descends into a drained lake). Inuit natives inhabit the area. With diamond demand sharply depressed by the economic turmoil in Asia, it would seem an inopportune time to open a big mine. But BHP Diamonds president Jim Rothwell vows the mine will begin earning a profit from the day the first stones go on sale in Antwerp this month. Who will buy the rough? Officially,