As an outcome of the books Louck (Los Alamos National Laboratory) and Biedenharm published in the 1980s, one plan was to extend the results for SU2 (which is a quantum mechanical rotation group of 2x2 unitary unimodular matrices) to the general unitary group U(n), based on their 30 years of collaboration. Louck became interested in the combinatorial basis of group representation and tensor operator theory, but has taken time after Biedenharm's death to fully develop their idea. His topics include quantum angular momentum, including combinatorial features, composite systems, including binary coupling theory, graphs and adjacency diagrams, including nonisomorphic trivalent trees and cubic graphs, generating functions, the form of certain polynomials, operator actions in Hilbert space, structure of certain polynomials, the general linear and unitary groups, tensor operator theory, basic algebraic objects, and combinatorial objects. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)