A pattern calculus for tensor operators in the unitary groups

Abstract

For a large class of tensor operators inU(n), a surprisingly simple diagrammatic calculus of patterns is shown to exist; to each operator of this class a pattern may be assigned in terms of which thecomplete algebraic formula for all matrix elements may be read off directly. The class of operators includes all fundamental, elementary and extremal Wigner operators in allU(n). Application of the pattern calculus toward the explicit determination of all tensor operators is discussed.