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The solution of the eigenvalue problem of the Laplacian with the normal metric induced by the Killing form on homogeneous special orthogonal spaces SO(2n + 1)/SO(2n) is given. The corresponding inverse branching rule from SO(2n) to SO(2n + 1) is obtained.

THE LAPLACIAN ON HOMOGENEOUS SPECIAL ORTHOGONAL SPACES AND THE INVERSE BRANCHING RULE