A simple formalism of real irreducible tensorial sets of real bases is
proposed. The definition of the real bases, the coupling of the real
bases, and the transformation of the real bases in a group chain inclu
ding the three-dimensional rotation group and the molecular point grou
ps are studied. The double coset technique is used to derive the close
formulas for generating the coupling coefficients and the transformat
ion coefficients. (C) 1996 John Wiley & Sons, Inc.