The Gel'fand basis and matrix elements of the graded unitary group U(m/n)

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Abstract
Projection operators with correct normalisation are constructed for obtaining the Gel'fand basis mod (( nu )(m))) of the graded unitary group U(m/n). Each U(m/n) Gel'fand basis vector mod (( nu )(m))) for an f-particle system uniquely corresponds to a non-standard basis vector mod ( nu )(m)) of the permutation group S(f). The matrix element of the generator Ei-1i of U(m/n) between the two Gel'fand basis vectors mod (( nu )(m))) and mod (( nu )(m))) is proportional to the overlap between the two non-standard basis vectors mod ( nu )(m')) and mod ( nu )(m)) of S(f). Explicit formulae are given for the normalisation constant in the projection operator as well as for the matrix elements of the generator Ei-1i of the graded unitary group U(m/n), which is the extension of the Gel'fand-Tsetlin formula for the ordinary unitary group U(m).