  Based on the direct-sum-decomposition of the rth tensor power of the defining
representation of the special orthogonal group SO(2k+1) one is interested in a
bijective approach for determining the Frobenius characters of the isotypic
components. In particular this leads us to a bijection between vacillating
tableaux and pairs of standard Young tableaux and orthogonal
Littlewood-Richardson tableaux, which we present for SO(3). Moreover we
introduce the descent set of a vacillating tableau. As our bijection preserves
this descent set, we also obtain the quasi-symmetric expansion of the Frobenius
characters.
