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The comedy focuses on a professor who witnesses his life fall apart when his wife leaves him and his brother refuses to move out of his home.
A Serious Man commenced filming in Minnesota this month, with Michael Stuhlbarg and Richard Kind playing the brothers.
Arkin, whose character is called Don Milgram, is a regular on NBC's crime series Life.
The Coens' next film Burn After Reading arrives in UK cinemas on October 27.
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