Spinor group and its restrictions

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Abstract
A realization of the spinor algebra of the rotation group SO(N), N=2n or 2n+1, in the covering algebra of U(2n) is exploited to obtain explicit representation matrices for the SO(N) generators in the basis adapted to the subgroup chain SO(N)⊃U(n)⊇U(n−1)⊃⋅⋅⋅⊃U(1). As a special case the computation of matrices of U(n) representations characterized by a k-column Young tableau is reduced to the evaluation of at most k-box totally symmetric representations of U(2n).