From a team standpoint, the National Invitation Tournament is supposed to be a frolic. It is a walk up Fifth Avenue and a chance to play in Madison Square Garden for teams that were good but not quite good enough to make the NCAA basketball tournament.

There is not supposed to be pressure on anybody at the NIT. But brilliant center Joe Barry Carroll and his Purdue teammates find themselves in something of a predicament heading into Wednesday's 9 p.m. championship game against Indiana (WTTG-TV-5, 11 p.m., delayed).

The Boilermakers would tarnish their big Ten trichampionship if they lost this rubber match to conference and intrastate rival Indiana.

Defeat is possible if defensive specialist Arnette Hallman cannot play well enough on one good foot to contain Indiana's Mike Woodson. Purdue is even more likely to lose if the officials do not keep a close watch inside for fouls committed against the 7-foot-1 Carroll, who will have so many people on him that he may ask to see boarding passes.

Purdue, which was picked in the preseason to finish seventh in its conference, earned a share of the title with Iowa and Michigan State largely because Carroll emerged as an offensive star.

Purdue's 27-7 overall record is second best in the Big Ten, but the Boiler-makers were not invited to the NCAA tournament because their record against Iowa and Michigan State was 1-3, and the NCAA takes only two from a conference.

Hours after new Coach Lee Rose learned he was not going to the NCAA tournament, he received and accepted, with something less than glee, a bid to the NIT. He had nothing against the NIT, but there was great disappointment in not going to the NCAA.

Bobby Knight, on the other hand, happily came to New York. His team is 21-12 and certainly has everything to gain by knocking off Purdue in the last game of the year, the one everyone will remember. This may not be a big deal to New Yorkers, but in Indiana, where these two coaches work, it is a very big deal.

Knight has made sure that he and his team will receive ample national recognition if they win, although most of the year Knight would not talk to the press after games.

Here, Knight has given interviews. He has answered questions, told jokes and gushed over the NIT. He has been sincere and entertaining, which he is capable of when something worthwhile is at stake, like the attention of the New York-based, national media. He was similarly charming at a press conference the day before he won his 1976 NCAA championship in Philadelphia.

But for Purdue, the NIT is pressure. Not just pressure to defend its part of the conference title.

The NIT committee has leaned heavily on Rose to make Carroll talk to the press although Carroll has not consented to be interviewed in his three years at Purdue.

According to those who know him, Carroll is a bright, sensitive person who does not understand why people want to pry into his private life. And his mother, who reared him and 10 other children, does not want Carroll to answer prying questions.

But those close to Carroll call him a leader and Purdue people believe he will speak up when the time is right.

In the meantime, the NIT has accidentally provided Purdue a chance to come out looking bad, after its most successful season since the 1969 squad made it to the NCAA tournament final.