Quantum-group Theoretical Extension of Rotation Group・Symmetric Group and Its Application to Many-body Problems

将关于角动量的Wigner-racah代数推广到量子(q-)群代数，使得张量(物理量)和生成元应该根据q-空间中的坐标变换以q-协变的方式变换。这种形式主义建议将其应用于核物理中的多体理论。在对称群特征标上研究了新的Q-形变。主要结果总结如下：系统地研究了玻色子/费米子产生湮灭算符的q-扩张，发现了q-扩张的第一类3nj符号与人脸模型的Yang-Baxter关系之间的新关系，得到了q-Clebsch-Gordan(q-CG)和q-racah系数等各种q-函数在q*1处的一阶和二阶导数的简单表达式。它系统地发现了3nj符号上新的恒等式。发现了一种新的q-变形对称群特征标，其中n&lt；小于等于-gt；5。这种基于物理模型的q-扩张本质上不同于通常的Hecke符号所固有的q-特征标。发现了使用与SU(2)相同类型的正交性的q-CG系数作为螺旋度表示、伪LS耦合等形式中的变换系数。

Wigner-Racah algebras on angular momentum are extended to quantum (q-) group algebras so that the tensors (physical quantities) as well as the generators should be transformed in q-covariant way according to coordinate transformation in q-space. This formalism suggests application to many-body theory in nuclear physics. New q-deformation is investigated also on symmetric group characters. Main results are summarized as follows :Systematic q-extension of Boson/Fermion creation-annihilation operators.New relationship is found between q-extended 3nj symbol of the first kind (which the author exploited) and Yang-Baxter relation of the face model.Remarkably simply expressions are obtained for the first and the second differential coefficients by q at q*1 of various q-functions such as q-Clebsch-Gordan (q-CG) and q-Racah coefficients. It leads to new systematic finding of novel identities on 3nj symbols.A new type of q-deformed symmetric group characters is found for Sn with n<less than or equal>5. This q-extension, which is based on a physical model, is essentially different from usual q-characters inherent to Hecke alPossibilities are found to use q-CG coefficients, which satisfy the same types of orthogonalities as those of SU (2), as transformation coefficients in helicity representation, pseudo LS coupling, etc.of the usual formalism.