QUANTUM GROUP SYMMETRY AND Q-TENSOR ALGEBRAS

Quantum groups are a generalization of the classical Liegroups and Lie algebras and provide a natural extension of the conceptof symmetry fundamental to physics. This monograph is a survey of themajor developments in quantum groups, using an original approach basedon the fundamental concept of a tensor operator. Using this concept,properties of both the algebra and co-algebra are developed from asingle uniform point of view, which is especially helpful forunderstanding the noncommuting co-ordinates of the quantum plane,which we interpret as elementary tensor operators. Representations ofthe q-deformed angular momentum group are discussed, including thecase where q is a root of unity, and general results are obtained forall unitary quantum groups using the method of algebraicinduction. Tensor operators are defined and discussed with examples,and a systematic treatment of the important (3j ) series of operatorsis developed in detail. This book is a good reference for graduatestudents in physics and mathematics.