Committee assignments - and chairs - are made by the parties. Murkowski, if reelected as an Independent, will probably caucus will the Republicans (as Lieberman does with the Democrats) but that is not certain. At any rate, they may not put her back there. The Washington Post quoted Jim DeMint (R-S.C.) on September 23d as saying(in reference to her not being removed now from the Senate Energy and Natural Resources Committee):

"It was bad enough to watch my colleagues work to support her in the primary after she had built a record of betraying conservatives principles," wrote DeMint. "But watching them back her after she left the party and launched a campaign against the Republican nominee was more than I could bear."