The Racah algebra for groups with time reversal symmetry

Abstract

The elements of the Racah algebra for a general compact group with time reversal symmetry are developed. As time reversal is antilinear it is not possible to treat these groups by representation theory but we may instead use Wigner's theory of corepresentations. The results we obtain often parallel those for linear groups but there are some important divergences. We illustrate these with the grey double point groups. © 1981 American Institute of Physics.