Matrix elements and Wigner coefficients for U q[gl(n)

Abstract

In this series of papers the fundamental Wigner coefficients and the matrix elements of the generators for the quantum group Uq[gl(n)] are derived. The Uq[gl(n)]:Uq[gl(n−1)] reduced Wigner coefficients and reduced matrix elements are determined algebraically as eigenvalues of certain Uq[gl(n−1)] invariants in the quantum group Uq[gl(n)]. The matrix elements of the elementary quantum group generators, in the Gel’fand–Tsetlin basis, are derived below, while all fundamental Wigner coefficients are derived in the second paper of the series.