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Based on the direct-sum-decomposition of the rth tensor power of the definingrepresentation of the special orthogonal group SO(2k+1) one is interested in abijective approach for determining the Frobenius characters of the isotypiccomponents. In particular this leads us to a bijection between vacillatingtableaux and pairs of standard Young tableaux and orthogonalLittlewood-Richardson tableaux, which we present for SO(3). Moreover weintroduce the descent set of a vacillating tableau. As our bijection preservesthis descent set, we also obtain the quasi-symmetric expansion of the Frobeniuscharacters.

A Sundaram type bijection for SO(3): vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux