A note on matrix elements of finiteU(n) transformations

Matrix elements of finite transformations of the group U(n) in an arbitrary unitary irreducible representation of U(n) are discussed and a technique for their determination is presented. As a by-product a recursion relation for a special Racah coefficient of U(n) is obtained.Work supported by the Comisión de Energia Nuclear, Mexico.Almost the whole work was done at theInternational Centre for Theoretical Physics, Trieste, Italy.We would like to thank Prof. Abdus Salam and Prof. P. Budini as well as the International Atomic Energy Agency for their hospitality at the I.C.T.P., Trieste. One of us (J. F.) would like to express his thanks to Prof. M. Moshinsky for helpful comments.