  We develop a classification of composite operators without gradients at
Anderson-transition critical points in disordered systems. These operators
represent correlation functions of the local density of states (or of
wave-function amplitudes). Our classification is motivated by the Iwasawa
decomposition for the field of the pertinent supersymmetric \sigma-model: the
scaling operators are represented by "plane waves" in terms of the
corresponding radial coordinates. We also present an alternative construction
of scaling operators by using the notion of highest-weight vector. We further
argue that a certain Weyl-group invariance associated with the \sigma-model
manifold leads to numerous exact symmetry relations between the scaling
dimensions of the composite operators. These symmetry relations generalize
those derived earlier for the multifractal spectrum of the leading operators.
