It's the Mycenaean Warrior Vase. About 12C BC,or maybe 7C BC. In a lot of schoolbooks (and the National Archaeological Museum at Athens). They're going off to war. She is waving a sad farewell.
But wait a minute. Would anybody go off to a real war in that goofy getup? And that sad farewell--don't I detect at least the hint of a smirk?
My guess is that they are off for an afternoon with the Society for Creative Anachronism. And she is relieved to get them out of the house, so she can finally get some work done.