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

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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.