The show’s most teasing joke is having the career pacifist John Hume (Dan Gordon), the gentlest pol in the room, ask the audience whether there’s any need for him to explain an elusive central point yet again. Whereupon he does not clarify.

“You all get it, don’t you?” Hume says, moving briskly along. “And if you haven’t — pay attention!”

In the rushing current of this play, what buoys us isn’t the particularities but rather the personalities. Mo Mowlam (Andrea Irvine), the flagrantly unpretentious British secretary of state for Northern Ireland and the only woman in the mix; Gerry Adams (Chris Corrigan), the leader of Sinn Fein, the political wing of the Irish Republican Army, who turns out to be good for a wisecrack at a urinal; Bertie Ahern (Ronan Leahy), the Irish premier, freshly in mourning for his mother and showing up anyway — this is a charismatic bunch.

With the American special envoy George Mitchell (Richard Croxford), the former Senator, as a kind of interloper-facilitator, they are quite likable, mostly, despite Blair (Martin Hutson) being besotted with his smiley self, and the men’s sexist sidelining of Mowlam. Her lack of vanity is in stark contrast to the obstructive male egotism on display. Radiation treatments have made her hair fall out, but when her wig gets too hot, she takes it off. Puts her stocking feet up on her desk, too.

The most maddeningly intransigent negotiator is the pinstriped David Trimble (Ruairi Conaghan), soon to become first minister of Northern Ireland. He is alienating in his stubbornness, yet he and Hume will share that year’s Nobel Peace Prize.

In honoring the healing accord reached in Belfast, the Nobel Committee said it hoped “that the foundations which have now been laid will not only lead to lasting peace in Northern Ireland, but also serve to inspire peaceful solutions to other religious, ethnic and national conflicts around the world.”