Budget Amount *help 
¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1993 : ¥100,000 (Direct Cost : ¥100,000)
Fiscal Year 1992 : ¥200,000 (Direct Cost : ¥200,000)
Fiscal Year 1991 : ¥700,000 (Direct Cost : ¥700,000)

Research Abstract 
We have widely extended the theory of angular momentum i.e.representation theory of rotation group, called WignerRacah algebras. Mathematical devices are devoted mainly to quantum (q) group algebras. Physical space of concern is socalled qspace, a noncommutative one, which is an extension of the prevalent commutative space. We have succeeded to specify all the quantities and their relations in the framework of qcovariant/contravariant forms. It is along the line of our postulate that any observable quantity (transition probability) should not rely on a certain linear coordinate transformation (qlinear transformation) of the qspace. According to the qcovariance, all the quantities are properly classified as qtensors (qscalar, qvector, etc.). We have qWignerEckart theorem, which is an extension of wellknown central theorem by Wigner and Eckart, and notions of qunit tensors in a very natural way. We have investigated kinds of basis functions, such as qrotation functions, qClebshGordan coefficients, qRacah coefficients (or, generally qnj symbols), and have established various relationship among them. Emphasis has been put on the point that these qfunctions form a class of basis functions constituting YangBaxter relations of face models and of vertex models. Further, we have found a systematic way to specify qcommutation relations among extended creationannihilation operators of qbosons and qfermions. There are several ways to assign the qcreation and annihilation operators to form spinors in the qcovariant theory. For example, we describe a qspinor in terms of a pair of creation and annihilation operators to obtain qanalog BCS Bogoliubov formalism. Using this result, we have succeeded to extend socalled symplecton algebras. We have generalized a part of the above consideration to the case of U_q(n). We have found also very new kinds of qextended Young diagrams (Schur functions).
