That would be Gosposvetsko polje ("field of the holy lady"). This is the location of the Ducal stone and throne. Unfortunately, the fascists moved the Ducal stone to the town hall in Celovec so I couldn't take a photo. This is where the democratic traditions of Carantania took place. Each municipality (župa) voted on which noble they thought was most suitable to lead them. Their representative (mayor - župan) would then go to Gosposvetsko polje and relay their vote - this is where the Americans got their electors from. A free farmer (kosez) sat on the stone (an upside down piece of a Roman column from the nearby city of Virunum, the capital of the Roman province of Noricum). The nobleman who was elected to be the duke approached him wearing peasant's clothes, to represent that he was chosen by the people to lead the people. He had to swear that he would rule in a just and fair way. He gave the farmer some cattle and then he was allowed to sit on the ducal throne. This whole coronation was in Slovene, even in the 16th century, after the Habsburgs became rulers.
Pictured here is the ducal throne. It was built from material brought from the city of Virunum.