The complaints deal with statements Kavanaugh made during his confirmation hearings.
The new justice dived into his new job, asking a handful of questions in the first arguments of the day following a traditional welcome from Chief Justice John Roberts, who wished Kavanaugh "a long and happy career in our common calling". The Senate never acted on Garland's Supreme Court nomination.
"There is nothing that a judicial council could do at this point", said Arthur Hellman, a law professor at the University of Pittsburgh and expert on the operation of federal courts.
The specifics of the complaints remain unknown, but people familiar with the matter say that they accuse Kavanaugh of misleading the public, and criticize his attitude and lack of political impartiality during his confirmation hearings. He said the 10th Circuit would probably close the case because it is outside of its jurisdiction now that Kavanaugh is a Supreme Court justice. The spectacle, in which more accusers and corroborators came forward, nearly derailed Kavanaugh's nomination.
Roberts' letter was sent to Judge Timothy Tymkovich, the 10th Circuit's chief judge.
Judge Karen LeCraft Henderson, a George H.W. Bush nominee, forwarded more than a dozen misconduct complaints to the chief justice after determining they were substantive enough that they needed to be investigated by judges outside the 2nd Circuit Court of Appeals, where Kavanaugh was serving as a judge.
Roberts received the first transfer request on September 20, followed by four additional requests on September 26, Sept. 28, October 3 and October 5, according to his letter.
But Gillers said the complaints "may be found not to be meritorious in the end".
Brett Kavanaugh took the bench with his new Supreme Court colleagues for the first time Tuesday in a jovial atmosphere that was strikingly at odds with the tension and rancor surrounding his high-court confirmation.
Henderson said members of the general public had filed the complaints. Details of the complaints have not been made public.
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