NEW YORK, DEC. 6 -- If President Reagan really wants to show Mikhail Gorbachev a slice of Americana, he might be well-advised to pull the tapes from Saturday's first "Big Four Classic" in the Indianapolis Hoosier Dome.

With four excellent, tradition-laden teams brought together for the doubleheader, 43,601 fans, all of them seemingly wearing their school colors, showed up for an afternoon of wonderful basketball.

Indiana, Notre Dame, Louisville and Kentucky are all less than 150 miles from Indianapolis, so the setting had the atmosphere of a Final Four. And the basketball was just about as good. Kentucky, one of the most improved teams in the country, may be ranked No. 1 this week after its bruising, 82-76, overtime victory over Indiana. And Notre Dame once again exposed the weakness of Louisville's guards as David Rivers put on a 32-point, seven-rebound show in a 69-54 romp.

Some final notes from the afternoon:Louisville freshman guard LaBradford Smith, considered the top high school guard in the country a year ago, has loads of potential but a long way to go. He had three points, was one for five from the field, and fouled out shortly after catching an elbow on his eyelid that resulted in six stitches.

"I thought I was doing okay," Smith said. "But I guess I didn't. I've got a lot to learn."

He will learn but he is still not the point guard Denny Crum needs, being more of a wing player. Louisville could be in for a very tough month with Kentucky and Indiana coming up the next two Saturdays. Against Notre Dame, the Cardinals played defense as if touching an Irish uniform would send an electric shock through their bodies.Each school left with about $350,000 including the money ABC-TV paid to televise the doubleheader. This is the first year of a four-year contract. There has been talk of turning this into a tournament -- Crum and Indiana's Bob Knight favor such a plan -- but in all likelihood it will remain a one-day extravaganza with the schools trading opponents but never meeting their in-state rivals. Next year it will be Indiana-Louisville and Notre Dame-Kentucky.Next year, the entire Hoosier Dome will be used for the doubleheader, meaning the crowd will be about 65,000. This year there was no public sale of tickets. Think people in the two states like their basketball?A Different GW?

George Washington let an upset get away against South Carolina Monday at home but came back Saturday to win in one of the toughest places in the country to play, Jenison Field House, upsetting Michigan State, 65-64.

Coach John Kuester and his players vowed after the loss Monday that this season would be different -- that GW would begin to win some of these tight games. Saturday, they did just that against a big-time team, on the road. Tuesday's game at home with George Mason should be interesting . . .

The game of the week had to be at De Paul Tuesday night. The Blue Demons had finally gained control against Niagara, leading by 88-80 with 15 seconds left in overtime.

In a scramble for a loose ball, De Paul's Terence Green was fouled. He lost his temper, threw a punch and was assessed a technical -- and ejected. Teammate Kevin Golden raced from the bench to join the fight -- another technical. Coach Joey Meyer sent freshman Brad Niemann in to shoot the one-and-one for Green. It made sense: Niemann shot 95 percent from the line in high school, once making 76 in a row.

Naturally, he missed. Niagara made all four technicals, inbounded and made a three-pointer with nine seconds left. Suddenly, it was 88-87. The Eagles immediately fouled Niemann again. Amazingly, he missed again. Niagara got an open jumper at the buzzer, but Stanley Grundy blocked the shot as time ran out and De Paul escaped the upset . . .

Tennessee opened its 25,435-seat arena Thursday -- the largest on-campus facility in the country -- after four years of hassles, delays, lawsuits and tragedy.

The Thomas-Boling Assembly Center, which cost $37 million, opened almost two years late with the Volunteers' 82-56 victory over Marquette. In that time Tennessee fired the original construction company and sued USF&G, the firm's underwriter, for $107 million. The construction firm itself has sued Tennessee for $2.7 million. One construction worker was killed in an accident and on opening night, overuse of the bathrooms caused flooding in the locker rooms.

In October, B. Ray Thompson, the man whose $5 million contribution -- anonymous at the time -- started the building, died of cancer, never seeing it open . . .

Jarrod Mustaf, one of the few top prep players in the country who did not sign in November, has narrowed his list of schools to three -- Maryland, Georgia Tech and Howard. The 6-9 DeMatha senior has taken official visits to Maryland and Howard. Word is he is leaning toward Maryland.The Upset Pick

The Upset Pick got off to a flying start Monday when Arizona beat Syracuse. But Saturday Xavier managed to lose to a Marquette team that looked awful against Tennessee. Such are the fates in Upset Picking. The record is 1-1. This week: two picks again -- Rhode Island goes to Philadelphia Saturday and stuns Temple and, midweek, Loyola Marymount goes to Oregon State and gives the Pacific-10 one more black eye.