  We compute the spectra of the Tanaka type Laplacians on the Rumin complex, a
quotient of the tangential Cauchy-Riemann complex on the unit sphere in $C^n$.
We prove that Szeg\"o map is a unitary operator from a subspace of $(p,
q-1)$-forms on the sphere defined by the Tanaka operators and the normal vector
field onto the space of $L^2$-harmonic $(p, q)$-forms on the unit ball. Our
results generalize earlier result of Folland.
