The university self-imposed some penalties, including the loss of one scholarship this season.

“Something has to be done because there’s a dark fog hanging over our university,” the former UConn and N.B.A. player Ray Allen said in June, according to The New Haven Register. Allen was deposed in the dispute, the newspaper said, because of a FaceTime conversation he had with a recruit that was a part of Ollie’s violations. “It’s tarnished who we are and where we hope to go in our future,” Allen said.

Before it plays in the Big East next year, UConn is playing one final, potentially awkward transitional year in the American, where it was picked by coaches to finish in the middle of the pack. The Huskies (6-2) are scheduled to play Indiana (8-1) on Tuesday night in the Jimmy V Classic at Madison Square Garden.

“There’s not going to be a lot of hugs and tears on our departure, so let’s use that as fuel,” Hurley said. “They’re probably going to stuff us in some worse locker rooms in arenas. We’ll get some people yelling some stuff at us, so we’ll use that as fuel. But don’t harp on what the last three years have been like here, that’s not our burden to carry.”

Javonte Brown-Ferguson, a 7-footer from Toronto, verbally committed to UConn last month, saying the Big East tournament at the Garden was a decisive factor.

“My family can drive down,” he said. “It’s a five-hour drive. Playing at Madison Square Garden, that’s just crazy thinking about it.”

For UConn’s powerhouse women’s basketball program, the change will be more subtle.

“We’re kind of used to being the bad guys everywhere we go,” said Coach Geno Auriemma, whose team is ranked No. 2 in the latest Associated Press Top 25 poll. “It’s always we’re the team that everybody loves to hate and wants to beat.”

Success for UConn’s women’s team includes a long history in the Big East, including eight national championships while a part of the conference.