NEW HAVEN, Conn. — This should be the Yale Bulldogs’ crowning moment — after a 54-year wait, the men’s basketball team brought an unshared Ivy League title home and with it an invitation to the N.C.A.A. tournament.

Instead, the team finds itself at odds with many students here over its continued support for its captain, a senior who left the university last month without a public explanation from anyone associated with Yale’s athletics department or its administration.

The departure of the player, Jack Montague, 22, was in connection with a sexual misconduct accusation, according to two people with direct knowledge of the case who spoke on condition of anonymity because of the confidential nature in which it was handled.

With protests on campus against the Bulldogs increasing, the team on Wednesday issued a statement apologizing for its public shows of support for Montague, which had included wearing shirts with his name and number during a game and making hand gestures signifying his number.