I'm looking for information on a short story that I read back in the mid-to-late 1980s.
"Trader's Cross" by Charles Sheffield in the March 1987 Analog.
The basic premise is that a general nuclear exchange has rendered most of Earth's surface uninhabitable, but small populations survived because they were in remote areas and were well-prepared. These populations have diverged culturally based on how they avoided extinction - there's a culture descended from people who were on a space station, and they stay in space, and another that lives tunneled into the ice in Antarctica.
"Most Trainees believe the Chips are the most alien of the groups," Dalzell had said, just before I boarded my plane, "simply because they live off-Earth. But for my money the Chills make 'em look like our brothers and sisters. Don't forget how the Chills got their start. Talk about evolution the hard way! Four thousand scientists, invaded by a million refugees fleeing south to avoid the fallout clouds. They started out with no food supplies and no energy—in a place where plants don't grow and solar power is useless. That's something to remember, in all your discussions with them. When the people you'll be negotiating with were children they were half-starved, every one of 'em. They had vitamin deficiencies, and they were dirty--no spare energy for luxuries like hot water. Never forget the Chills are different." He rolled one of his sleeves all the way up to the shoulder, to reveal a long, deep scar. "Here's an example of what can happen when Chill negotiation goes wrong. It took me totally by surprise. Until one of the Chills put a dart through my arm, I thought I had everything under perfect control. But I made a joke about a penguin not being sure if it was a bird or a fish. And I got this. The others took her away after she did it, and I never saw her again. I'll give you a Trader's Rule that you'll not see in the rule book: Never make a joke to a Chill."
The protagonist is from a cultural group that functions variously as traders, diplomats, negotiators, and spies.
"Damn right." Dalzell's gruff voice sounded delighted with my reply. "And that's the answer I was hoping for. So let's get down to it. Mike Asparian, I can tell you now, you'll need to be good. We're talking of an official mission down onto the ice cap, to the middle of Chill territory. You'll need to be one hot-shot negotiator. The Unified Empire wants us to act on its behalf for a ten-year deal on gaming-table robot controllers. The Greasers are finally admitting what I've been telling 'em for fifteen years—the Chills are so far ahead of everybody else in micro-electronics that nobody else has a hope of competing. Apparently it's finally sunk into their thick Greaser skulls, and they called me ten days ago. I set out terms they can live with, and I'm fairly sure the Chills will go along with them."
He's hired to retrieve an idiot savant who was kidnapped by the Antarctic culture
"You see, Mike, Seth Paramine isn't up in Yankeeland any more. He's down on the ice cap. The Chills are the world experts on microcircuit design, and somehow they heard about him. They wanted him. They took him. Four days ago, Seth Paramine disappeared from the Institution. He hasn't been heard from since--but all the evidence suggests a Chill smash operation. They're damn near as good at rapid, quiet pick-up as we are."
due to his odd talent of understanding electronic circuit logic simply by looking at it.
"Seth Paramine is one of that rare group of people, the idiot savants. And he is a spectacular example. Those cardboard sheets are electronic schematics—circuit diagrams, blown up thousands of times over their original dimensions. They came from Chill micro-circuits, and they're the most advanced gadgets on the market. What you saw there was Seth Paramine studying the designs--and improving them. He can't write his name. He wears diapers. In every area of the world except one, he's a complete idiot. But he has an intuitive grasp of micro-circuit functional design that no one else can understand or equal. In circuit design, he's a genius."
I'm pretty sure I read it in a pulp magazine that also contained part of a serialization of Larry Niven's The Smoke Ring.
Yes, part 3 of the four-part serial is in that issue of Analog.